I honestly think there is more in common there than people would like to assume.
I've heard NB people explain that in their mind the gendered stereotypes, gender roles etc are ludicrous, for 99% of interactions it makes no difference what your sex (or gender) is - only really for medical issues and sexual partners - and identifying as NB is a way to essentially say "What's it to you? Why does it matter anyway?" They think that this is unpalatable to a lot of people because many people are wedded to gendered norms and feel that it IS important to know if somebody is male or female when having daily interactions with them.
I think most feminists would agree totally with the premise that your sex should not matter in matters of e.g. work, fashion choices, friendships, driving licence and so on.
Where the disagreement lies is that the NB/genderfluid movement thinks that the way to change this and prove that sex/gender is irrelevant is to actively challenge gender norms and rules by saying well - why can't I (a bio male) be female? Why do I need to specify at all, I'm NB. My understanding is that this is seen as one step in the process of "expanding ideas and definitions of gender". With the end goal being that gender isn't really even a thing, much like nobody thinks that blood type means anything relevant most of the time and wouldn't even think to ask someone what their blood type is, except in a medical situation.
Whereas old school/radical feminists say hang on, but it does matter because sexism and patriarchy exists. Although it makes sense that sex should not matter for interactions outside of medicine and sex, in reality it does, and that is the whole problem. We should not obscure that by confusing things with new titles (NB) or by changing definitions of what words mean (male/female being identities rather than biological reality). We actually need clear language and definitions in order that these patterns can be discussed, studied and so on.
I think there's also a clash in that old school/RFs can see the NB stuff as a load of new fangled nonsense that doesn't make sense and perpetuates the problem - which can come across as offensive to NB people. But the main thing is frustration that "the gender crowd" want to obfuscate language, as they see the most urgent issue as making sexism more visible and clear to everyone, seeing that as the way to change things, and they think that the whole "expanding gender roles" approach gets in the way of this.
And the gender crowd misunderstand the GC feminists' desire to insist on biological language, as they see this as essentialist and trapping people in roles.