Yes, but it's usually in the context of certain gender roles that are very obviously social. Women did not evolve to look like modern Western feminine women, such a thing simply isn't possible. Wearing a hijab makes some women "feel like a woman". Having long hair makes women "feel like a woman". Women weren't born with long hair and hijab skin flaps covering them, these are social expectations placed on them, usually to a woman's detriment.

Certainly men and women are raised to "feel more like a man/woman" through emulating patriarchal norms that are damaging to women. You might speak of "gender identity" in that way, but we already have "gender roles" for that. This should be considered unhealthy and sexist in any actual feminist movement.