It is entirely possible to be a feminist without accepting the theories/tenets of patriarchy. Feminism, in the broadest sense, is the recognition that women in general (not every individual woman) have a lower status in society (also termed “women’s oppression”), and that women in general have an interest in fighting against that.
Patriarchy is one theory that attempts to explain why women in general are oppressed - it argues either that it’s biological or genetic or evolutionary, largely ignoring the fact that throughout history (and even today) there have been functional matriarchal societies as well as societies in which men and women enjoyed far more equality than they do today. There’s a lot of sociological and cultural evidence that women’s oppression isn’t hardwired into men’s brains.
Rape culture, on the other hand, isn’t quite as easy to dismiss. I wouldn’t argue that feminists have to accept the theory of rape culture, but it certainly should be examined more in-depth before taking a stand on it. And I’m not entirely convinced that rejecting it outright is a good conclusion to draw.
Rape culture theory points out a lot of undeniable facts, for example underreporting of cases of rape, “slut-shaming” when rape is reported, the portrayal of women as sex objects in almost every context in which they appear (two words: women’s volleyball). Couple this with the social pressure to view sex as an important yardstick in assessing the success of a relationship (or even social interaction) and you do end up with the potential for some men to refuse to take ‘no’ for an answer.
It apparently is possible to take rape culture theory to a patriarchal conclusion and blame all men for rape (going back to the biological or evolutionary argument again), but an illogical conclusion in and of itself does not invalidate the theory if it can be shown that the conclusion is the result of misunderstanding or misapplying the theory.