A lot of leftists have adopted the view that sex work is something positive, liberatory, just another type of work that should be supported like wholesome small businesses while ignoring the reality of just how fucked it is (the why on why it's fucked and why it's rapey is in my other comments), I'd argue more often than not this is done deliberately to justify their own unhealthy views.
The post + title combo and some background of OP of this post (not the tweet) makes me believe they are exactly this type of person, which is what I was responding to. I am not arguing that "sex workers are enemy of the working class", that's stupid and I highly doubt anyone sane or anyone here at all says that except some Marx quote which OP references if one was to read it in the most disingenuous way possible.
It is work, they are workers, but it's a horrible job that can easily be and must be abolished even before commodity form dies.
That being said:
But sex workers have to be centered in the project for their own liberation, as only they are able to liberate themselves.
Alright, with all due respect, what the fuck are you talking about? Workers struggle is one and the same, there are no "unique worker struggles". The historic task of proletariat is to abolish the anarchic mode of production, private property and commodity form completely (in other words, the current state of things) in favor of production for use in a classless, stateless society. Sex work would literally cease to be a thing, if someone truly wants to fuck a ton then they're not a prostitute but a 'playah' since no exchange takes place other than one of actual consent, with all the survival needs and freedoms being provided freely already.
Even as early as DOTP, there would be no reason to keep sex workers or lumpenproletariat in their positions given their misery and the ability for counter-revolutionaries to mobilize them. Reintegration to the labor pool is the most sane choice.
Without a proletarian revolution, there is no emancipation.
P.S. you use "division of labor" in the wrong way. What it refers to is not when workers go and cry about whose job is real or not, but a concept where people split into specialized roles during labor process. It is it's own can of worms that is completely unrelated to this topic.