Of course the dalish would make that judgment, they have an agenda. It suits their interests to deny Andrastian elves any legitimate identity for not adhering to the their particular ideals. Its a large part of the reason I don't like them.
Insisting as such is to support a racialized ideology of religious conformity. Shartan was Andrastian, Ameridan had his syncretism, it didn't stop them from reconciling being both Andrastian and elves. Even what the Chantry has done in the meantime doesn't change that reconciling the two is possible. It does not require elves to "pretend they are human" much as the dalish would love to delegitimize them.
I feel Sera showcases the other extreme, the people who say ''I don't care about X!'' so much you start suspecting they actually do care. She quite simply dislikes the Dalish and the associated ''elfyness''. She takes enough pains to distance herself from that identity that I don't truly believe she just wants to be ''people''.
As someone said, Zevran is really the only elf who did not let his race influence who he was in any way. He didn't need to remind everyone that he wasn't like these people and didn't like these people.
As for the break up, while the Inquisitor isn't the brightest person for trying to get together with a person who is quite vocal about disliking their people, Sera demanding that Quizzy change all that, up to pretty much forsaking a key part of their identity, is a really low blow. She's being incredibly selfish and immature here.
I don't know. Some people seem to think those traits make her quirky and likeable, more power to them. I just find her supremely annoying. I don't need my companions sucking up to me, but I draw the line at filfth flinging from a bratty teenager who can't accept that the world is more complicated than she thinks.