I was wondering the same exact thing, but to put it more specifically, is it possible to become a stream-entrant (not just a general Buddhist) without believing in rebirth--or even kamma? The pre-requisites for stream-entry appear to be quite clear: the elimination of three of the ten fetters, which include doubt about the dhamma. Since rebirth and kamma are pretty darn fundamental to the dhamma, I would imagine that most buddhists would say that even if someone were otherwise identical to a stream-entrant in every way in terms of behavior and mental states (I know, you could argue that this would be impossible without believing in dhamma and kamma), just the fact that one of them doesn't believe in kamma and rebirth means that they must not be a stream-entrant. This seems, to me, akin to Christians saying you'll go to hell if you don't accept Jesus Christ as your lord and savior.
This bothers me because I (at least at this point) cannot believe in these things. I'm sorry if this seems blasphemous or disrespectful to anyone, but I'm actually surprised that Buddha believed in these concepts. I know he comes from a different time and culture, but all of his teachings, with the exception of these two things, are completely experiential and provable. He even seems to advocate a sort of scientific method, encouraging people to try the teaching, and to reject it if it doesn't work. Kamma and rebirth, however, are completely, entirely unprovable, and, as with the existence of god, why bother yourself about something that is utterly unknowable and probably made-up? (I know the arguments in favor of kamma and rebirth, so no need to trouble yourself with trying to convince me otherwise.)
I DO, however, believe in those things in a more practical or metaphorical sense: if you don't follow the dhamma, you will be miserable. I've sure experienced that myself. And I see the end of rebirth as the end of the rebirth of desires. Since this is sufficient, to me, to agree with the rest of his teachings, shouldn't it be sufficient for stream-entry?
I feel like some people will feel compelled to answer with "why are you worried about this? You're so far from stream-entry anyway, just do the practice, etc." or "why are you so resistant? Why don't you examine that, etc.", but, to me, these sorts of answers shut down questioning and exploration, and Buddha himself answered questions thoroughly (most of the time), so I would just like to humbly request answers that aren't merely dismissive.