I think OP's understanding of GC feminism sounds pretty good.
One reason why I think GC theory attracts so much criticism is that a lot of liberal feminism up until about 2010 was about how women are not limited by our sex - a woman can be whatever she wants to be. That involved challenging a lot of gender stereotypes and biological determinism: for example the idea that it is 'natural' for a woman to stay home to take care of kids and give up her career; or that women are better suited to (low paid) caring roles, because we are 'naturally' more sensitive and nurturing; whilst men are 'naturally' competitive and good at maths.
Challenging these negative gender stereotypes meant challenging a lot of incorrect ideas about biology: no-one's womb falls out if they do sports; women are not biologically hardwired to enjoy housework or wearing high heels; if women are not equally represented in some careers, this is more likely to be caused by sexism than because we are biologically less capable.
Consequently, there's a lot of resistance within feminism and the left generally to re-centering sex-based, immutable biology: we've spent the last 60 years arguing that women are not defined by biology -- and that there's very little evidence to support biologically essentialist reasons for observed gender differences. We've used terminology that centres "gender" differences rather than "sex" differences, to highlight the importance of gendered socialisation, rather than biology, in explaining them. For example, yes, there are gender differences in (say) adult navigation ability, but most/all of that is accounted for by differences in socialisation. Yes, you can do fMRI brain scans and find sex differences (sometimes, maybe); but the brain changes with social experience. We usually call that 'learning'.
Therefore, when we hear "Yes, but men and women are biologically different", we are primed to hear a reductive argument about women's social roles: that the gender pay gap, lack of women in STEM subjects, or poor uptake of shared parental leave are caused by innate biological differences that cause women to be weaker and less able. And there are a depressingly large number of right-wing columnists and researchers who still make these arguments.
(And, to be fair, there is a fuzzy gray area in the middle. Physically, women are on average smaller, weaker and slower than men. That's why we have sex categories for sport. That means we may never achieve 50% sex-parity in specific professions where speed or strength matter a lot. And teasing out the different strands of influence on gendered behaviour is hugely complex. When you get into the weeds of various scientific studies, everything gets messy and unclear and shaped by the biases of the researchers themselves. Cordelia Fine's Delusions of Gender is really comprehensive on all this).
That makes it harder to get the point across: Yes, gender roles are socially constructed; no, we don't have to conform to them; yes, we can attract social censure when we don't; yes the way we see ourselves (our gender identity?) is influenced by our socialisation and includes elements of gendered preferences.
But that doesn't mean that biological sex doesn't exist. Or that we can reason it away with deconstructionist obfuscation. Women get pregnant. We menstruate. That matters. Having a woman's body makes some men feel entitled to use us for sex; to abuse us and rape us. Because we are women, we are socialised to put others' needs before our own. That matters too.
We took for granted the assumption that people know that biological sex exists. It didn't need saying, because it was obvious. And most liberal feminists still assume that focusing on biology is repressive and sexist.
Gradually, the "no sex, only gender" arguments have become more prominent. They use lots of the same vocabulary as liberal feminism; so feel like a natural progression of the "not defined by biology" argument. But it's not. And it's quite scary how hard it is to get this across without being silenced by people you thought were your friends.