Well, we can define assuming the social role of a woman in two ways: the first is going to be gender stereotypes and things GC generally don't like. As I said, even if you dislike those stereotypes, they still are there. MTF can mimic those stereotypes -- again I'd say Blaire White is a good example of this, her way of dress, makeup, personality, and mannerisms resemble a "stereotypical woman".

Secondly there is a physical/biological aspect to it, to the extent that MTF change their body (breasts, FFS, hormone balance etc) -- these are man made changes but they are material changes in one's body that makes people more likely to view them as female than as male. I think of the secondary sex characteristics in terms of beards and breasts -- if you see a person with a flat chest and a beard, almost everyone is going to call them "sir" even if the rest of their traits seem feminine/they are biologically female, because the beard so strongly signals "male" to people. (Yeah yeah GCers can tell I get it-- I'm talking about your average person on the street who hasn't thought very deeply about trans people and aren't particularly looking out for signs of that). Conversely if you see a clean shaven person with breasts, even if they seem male otherwise, the average person is going to assume they are a woman, because men simply don't have protruding breasts under normal circumstances.

For the second point, I fully agree and this is what actually drove me closer to GC than QT as a former full on "trans ally". However, it is important to note that not literally all trans women act the way you're describing. That's the loudest, most offensive way, and it's become the face of the trans rights movement (probably exactly because they are males that like to domineer discussions and center them around themselves). But there do exist trans women who do try to actually act like what society would expect of a woman-- we hear less from them because by definition they aren't bossy or loud. Many of these trans women call themselves transsexual and generally understand they're biologically male, they just have a serious mental condition (gender dysphoria) for which the best treatment available right now is transition. They're just living their lives as best they can. They don't wave their "girldicks" around because they don't like having a penis or other things about them that makes them "male"-- literally by definition, they feel dysphoric about their birth sex. These are also the trans women who shy away from sports or other contexts in which they would stand out for being biologically male, again because they don't want that brought to people's attention as it is a source of distress and shame for them.

I know these people exist because I had a very close friend with this condition. She would go to this alternative funky thrift store and buy piles of clothing second hand because she didn't want to be seen in a regular store buying women's clothing and certainly didn't want to go into a women's changing room before "passing", so she'd try them on at home. She quit doing sports except for casual intramural stuff that was co-ed. She always was up front about being trans when dating and she accepted that it would mean the majority of people would not be interested in her (she described it as going to a shoe store with wide feet-- the vast majority of shoes simply aren't made for you, and that might mean you only can choose from a few options). She did hormones, surgery(including bottom surgery), the works. Is she "really a woman"? Well, strictly speaking, no. But when she put so much effort into living life the way that she could feel most comfortable, and was always respectful of others, I just kinda feel like it'd be a dick move for me to constantly point out to her that she was born male. So people like that, to me, I can treat them as "women" and use female pronouns and such because in my view they clearly have made a good faith effort and are not harming biological women and if being polite helps relieve their mental distress at the current time where we don't have a way to relieve GD with medicine or therapy otherwise, then I'm going to do so.

In my view there is a tiny number of these people with gender dysphoria, who are harming no one. However, a large number of perverts, fetishists, "not like the other girls" snowflakes, white people who want to identify into oppression, and other trenders in general that have co-opted the struggle of transsexual people to further their own ends. My beef lies solely with them.