I think it's pretty obvious after the latest chapter it's the homosexuality she's anxious about, no? The cousin thing is also weird but I don't think I've ever seen cousin incest get stigmatized in anime/manga the same way that homosexuality does. If it was just about being cousins then there wouldn't be much of a reason to bring up the childhood crush like it was also 'abnormal' unless that was somehow a different cousin, which I feel would've been mentioned if that were the case.
Lots of yuri works go out of their way to avoid queer identity labels like "gay" and "lesbian," it's not all that unusual to see characters dance around terms like this.