It seems like it could in fact be a valid sexuality type to be attracted exclusively to sex rather than gender, but the only common term that seems to describe this sexuality is "super straight" (when referencing the heterosexual form of this, while "super gay" might be an unused but equivalent term for the homosexual form) which carries harmful connotations that aren't inherently entailed by having this sexuality type - which I agree is not a broader sexual orientation like heterosexual/homosexual/bisexual/asexual etc, but is more like a "microlabel" such as demisexual, in that it's an additional descriptor that further specifies the exact nature of someone's individual sexual preferences/orientation. However, that also doesn't mean it needs to be considered as part of the LGBTQ+ community, as it's not a marginalized sexuality or identity - in fact I'm pretty sure it's one of the most common sexuality types there are, if not the most common. Especially due to how stigmatized or misunderstood this sexuality is, or that people feel it's invalid or tied to discrimination against LGBT people somewhat inseparably, there isn't much research on it, so it's possible that people who are attracted to gender are more common than people who are attracted to sex, but it could be the opposite.
I understand the history of this word is problematic as it was created by transphobes, and its perception is so heavily tied to those origins that it's considered a hateful ideology in itself. That's one reason the word needs a different replacement and a "fresh start". People are identifying as this sexuality without any bigoted ideas toward LGBT people, even being vocally pro-LGBT, but simply having no other word to describe their exact sexuality, and then using this word despite it having other connotations they don't agree with, because it's the closest word there is - and then being misunderstood and criticized for using it. It seems like replacing this word with a more well-intentioned one would actually serve to hinder those hateful ideologies from spreading (by stopping people from resorting to using it with no other alternative, as is happening a lot) and enable people to acknowledge the validity of all sexual preferences or orientations as distinct from any hateful rhetoric.
Additionally, the word itself carries problematic connotations linguistically - even if it wasn't tied to attempts to undermine LGBT rights movements - since it could be interpreted as implying that people who are attracted to people of the opposite gender regardless of sex are "less straight" than people who are only attracted to the opposite sex regardless of gender. This recalls the fairly backward arguments (or offensive jokes) that someone who is attracted to people who were born as the same sex as them but who identify/present as the opposite gender, is actually "secretly gay" or "in denial of being gay" due to that attraction and is not really straight - that, for example, a man who is capable of being attracted to either cis women as well as trans women is therefore somehow less straight or more gay (or bi) than one who is only attracted to cis women - and this may come across as undermining the validity of those people as truly being the gender they identify as, or in other words attempting to deny or downplay the fact that trans women are women and trans men are men.
But it must be understood that being attracted to sex rather than gender does not mean denying the validity of gender identities in any way. Someone can fully support the rights of and acknowledge the legitimacy of trans people, that trans women are women and trans men are men in full, etc. The reality is just that sex is something distinct from gender and some people are attracted to one or the other or both, but not necessarily both. It's not something that can be entirely rationalized or explained, just like why someone is attracted to men rather than women or vice versa, or any other sexuality. It's something that people just naturally feel. Some so-called "super straight" people, non-bigoted and well-meaning ones in search of a way to explain and justify their sexual choices, genuinely just don't feel attraction to people who were born as the same sex as them, even if those people identify as/present as the opposite gender to them, and even while still considering them to be women/men in alignment with their gender etc. For the homosexual equivalent, aka "super gay", some people also are only attracted to their own sex, and would not be attracted to someone who was born as the opposite sex even if they identified/presented as the same gender as them. How can we criticize someone for having a particular sexual preference or orientation like that? I'm not saying they're oppressed or anything for having that nature (for being gay, yes, not for being "super gay" or "super straight"), but it seems silly and harmful to not be able to distinguish between people who are attracted to sex and people who are attracted to gender - it also doesn't need to be necessarily words based on how it relates to a larger orientation (like "super straight" and "super gay") but rather an additional label that you can place on any sexuality which denotes whether your attraction is gender-based or sex-based, or either, or both. To say that that is somehow discriminating against individuals just by not being attracted to them in some way you can't change - despite fully respecting them - seems no different from suggesting that someone is discriminating against women or men just by not being attracted to them since that's their sexuality. Are gay men necessarily misogynists? Of course not. So why would people who are attracted to cis people (of a particular sex) and not trans people (of the opposite sex-assigned-at-birth to the sex they're attracted to) necessarily be transphobes? It seems like there would be further variations to this as well depending on how people's exact sexuality cashes out.
The fact we can't seem to talk about this without assuming people have bad intentions, lumping them together with other people via association fallacies, and strawmanning people as being bigoted while misunderstanding or deliberately misrepresenting their experience/position is silly. It's obviously a nuanced subject, and human sexuality is complex. There could well be some unrecognized validity to a differentiation between sex-based vs gender-based attraction, and it seems like it would benefit the LGBT rights movements to be able to acknowledge these kinds of experiences, of people who are genuinely supportive of LGBT, rather than immediately demonizing it without trying to understand it. Maybe we can have a bit of good faith here?
(Btw, I don't identify with the super straight label nor with the sexuality type it describes even with the bigotry removed, but I don't find it to be justified to criticize people for having this particular experience of sexual attraction, and think it deserves a proper unproblematic term, or multiple words related to the larger concept of sex vs gender based attraction).
Ehhhh, I think you screwed up by over explaining. The point you're endlessly actually asking about makes sense, and it's a valid discussion to have, but it's buried when you're trying to ask something. There's a limit in the human brain to how much information you can track in a question before you start losing parts. There's one for raw information as well, but it's bigger and easier to bypass. I hope, because this is going to be a long response.
The reason that "super straight" is offensive is because it implies that attraction to a trans person isn't heterosexual when the expressed gender would make the attraction hetero. By the very fact that "super" is used as the modifier, it implies better as well. And that's just bullshit, which I think you pretty much said despite it being buried.
If you have some need to draw a distinction between heterosexuality that includes trans partners, it's inherently trans exclusionary. There's nothing wrong with not being attracted to trans people, it's when the implication is that there's a difference between heterosexuals that do and haven't experienced that attraction that you run into the wall.
However, for the purposes of discussing the matter, I think either cis-exclusive hetero or trans-exclusionary hetero would be the most effective terms cis-exclusive would mean that your attraction is limited to cis people, with no rejection of transness in that you would be expressing it as attraction first. Trans,exclusionary would be for those that reject transness ideologically or for reasons other than raw attraction.
Now, I think it important to note that a lack of attraction by itself doesn't mean anything else. It isn't some kind of glaring proof of bigotry. The way humans form attraction leads to the unfamiliar having a greater weight in what base attractions factor in. As an example, not being attracted to white people doesn't mean you're a bigot, it just means that the collective set of characteristics of white people doesn't match your inner "template".
Now, that template may well have been formed because of bigotry, be it internal or external, but it isn't the proof of the pudding. Just by virtue of growing up with little or no exposure to other physical traits than your own ethnicity can cause your template to be limited to those that look most like what you're used to. The unfamiliar is, on a primitive level, a questionable source for mates.
It's how people handle their templates that matters, not that they have them. If I say "white women are ugly", that's shitty, and a form of bigotry. If I say "I've never met a white woman that I've been attracted to", that's a statement of fact (well, not for me personally, this is an example, not a statement of my own preferences). Now, I could be saying it politely and still be a bigot, but saying it isn't proof of bigotry.
This applies to trans people too. Acknowledging that you've never felt attraction to a trans person is a statement. Saying that they're ugly is shitty, and is probably bigotry, depending on the reasoning. Saying they aren't women/men is bigotry.
So, the why matters more than actual terminology, which means that more options in terminology are helpful when discussing the matter in general. The two I suggested are already what I use in my head when thinking about the subject of attraction as a whole, and how transness factors into the individual "templates".
Now, as a personal example, I don't have many limits in terms of what kind of women I feel attraction to. Race has never factored in at all. The range of physical features I feel attraction to is very broad, and tends to be more about details than categories (like noses; size doesn't factor in, proportions do). As such, I can't ever say I wouldn't be attracted to a trans woman. I can, however, say that I would never be attracted to a trans man because I've never been attracted to a man. Tbh, I've never experienced attraction to anyone that strongly presented as male, even when I knew they were women. My inner template has an edge in the androgynous range of features and traits, and once it crosses into a perception of a person being a man/male, attraction goes away.
I included that as a comparison, because what/who I personally feel attraction to isn't the same as examples used. For the same reason, I specifically have experienced attraction to trans women, but never in a circumstance where it mattered. Thus, I don't fit either the cis-exclusive or trans-exclusionary labels, to the best of my self awareness.
Now, I get it. Trans identity is only fairly recently in general awareness. It's been in my lifetime that it went from being something even most bigots didn't really know existed (and they look for people to hate because that's their fetish, hate) to being something that's a topic of common discussion. So there's going to be people that just don't know enough to matter still talking about the subject. Ignorance isn't the same as hate, though they sometimes wear the same hat. That's where some if the things you talked about (l.e. "secretly gay") come from. They just don't get it.
That's why I agree that the term "super" straight/gay is bullshit and needs to go away. But there is room for terminology to indicate the layers of attraction in conversation, as long as people aren't being dicks about it