My thing is, society is at a contradictory crossroads concerning gender roles: on the one hand, there are those who seek to shake off restrictive notions of femininity and masculinity for both genders, saying that a woman can act more "masculine" or take on traditionally masculine roles, and a man can act more "feminine" and take on traditionally feminine roles. Essentially, men and women shouldn't be restricted by societal notions of how a "man" or "woman" should be. It is perfectly acceptable for a woman to "act like a man". As Judith Butler puts it, the gender roles and identities of men and women are improvisations that are shaped on the fly as a result of societal interaction, and are thus subject to change. To put it roughly, bodily anatomy is set in stone, but gender roles aren't.
On the other hand, I get the sense that people who insist on using pronouns that don't correspond to their biological sex do ascribe to the idea that there is a more concrete or immutable substance behind societal descriptors of how a man and woman should act. I have had trans people tell me that they know they're really a man or a woman, despite their anatomy, because they think like the opposite sex and they've never acted traditionally "masculine" or "feminine". It's the idea that one is a "man trapped in a woman's body" or vice-versa. So they feel they have to change their bodies to match. To put it roughly, gender identities are set in stone, but bodily anatomy isn't. So there is in fact a clear demarcation between being a man or a woman, or else transgender people would not feel a need to transition. I know at least a few transgender people who take special issue with Judith Butler for this very reason, because she would call such assumptions into question.
To me, these two ideologies are in conflict. I can understand why many feminists feel that transgender issues are incompatible with feminism.