I still have to pay attention to my words because I use gendered language reflexively from years of learned behavior (US English here) and I don't get it right all the time, so I'll be the first to say it's not only not weird to say "my wife" or the like, it is in fact far too damn easy for the words to just fall out on their own. It's been practice for me to get used to saying spouse and partner but I think it's good overall to omit the gendered aspect when it is irrelevant simply because the result is more inclusive language that resonates with an even larger audience.

We stopped including things like skin color and sexuality as an extraneous identifying detail in conversation a long while back (speaking in a really broad generality here, forgive me please) because people recognized it as othering. I feel like we're getting there with gendered language and like it's for the best.