Is there a term for this? May I suggest "wrongthink by associaton"?
Furthermore I suspect this is less about he/him vs she/hers but some of the more esoteric pronoun preferences.
I think this is a fairly descriptive term. This happened fairly recently for me in another context. After I saw Star Wars Episode VIII, I let it be known that I thought it was a bad movie. In this cultural moment, some folks will take that innocent opinion from a lifelong Star Wars fan as a signifier of my stance in favor of every controversial thing that a terrible person who also disliked the movie said. It feels like everything is taken as a dog whistle.
Is that the case here? I would think it is a bit too avantgardist to expect people to contort their sentences to include singular pronouns beyond he/she/they at this point. I get the impression that those esoteric made-up pronouns tend to be mostly used for straw-men arguments.