Maybe the common ground with some of the Christian right ( & most other religions; as well as with most of the rational world, in general) is a recognition that biological sex exists, and that it matters.
The divergence comes occurs when considering what exactly that biological sex means, and how it should be perceived and dealt with in everyday reality. Many on the right ( & religious right) believe that biology is absolute destiny; and that men & women should live according to strict or segregated social roles on account of that biology. Transgression of the rules is not permitted, and/or is punished in some way. Everyone is expected to conform to gendered norms and expectations.
The religious right in the U.S/the West is, slightly, an exception to this - because women can and do hold & perform social roles & functions that would not be permitted in other cultures and societies. However, essentialist ideas around biology and sex do matter - and so motherhood & family, for example, play an exalted role.
Feminism recognises that biological sex is a reality ( different strands of feminism differ in how they approach that, though); although generally it is believed that although biology obviously exists, it does not have to mean absolute destiny, in terms of developing a full range of personal expression: that social roles & expressions should be open to all who feel naturally able to fulfil them or embody them, regardless of biological sex.
It is understood that most socially constructed, & enforced, roles are given lesser value when & if performed by females. That the dominant value system arises from a male centred view of the world, that prioritises men and boys, and rewards them more- especially if they perform expected gender roles satisfactorily. Males, too, though, are punished if they step out of line; especially if they perform anything approaching 'femininity', no matter how 'natural' that feels for them.
My feminism has always ben a blend of individualism alongside biological celebration ( valuing the female biological functions, and some of the social roles that accompany those functions), although in my version women's traditional roles are valued equally to men's.
I recognise that parts of my temperament and nature are quite comfortable with my body and biology, though - and I have never really suffered from dysphoria ( apart from sometimes fancying having a different body shape to the one I'm in).