Yes, the heart of the gender identity movement IS deeply sexist, even misogynist.
Adding nonbinary to 'men' and 'women' as the categories inherently implies, given that there is no nonbinary sex category in humans, that now both 'men' and 'women' are also definitions based not on sex but on gender stereotypes.
So in order to be 'inclusive' and 'kind' to enbies, all others are ordered to view themselves as defined by sexist beliefs about femininity or masculinity and/or supposed comfort with retrogressive gender roles.
This is NOT inclusive or kind to us.
And it is almost as anti-feminist as the far right anti-feminist beliefs, because both expect 'women' to follow stereotypical retrogressive cultural rules, and it is those rules which sexism has always used to subjugate the female sex class.
The gender identitarians seem to expect us women to transition to, say, nonbinary, should we actually wish for equal treatment, but neither sexism nor misogyny are going to check for someone's preferred nonbinary pronouns before picking their prey. All they care about is based on sex.
And this makes the gender identity ideology deeply sexist, because the actual fee for being treated somewhat equally would have to be a full medical transition into a passing trans man.