I personally like to believe in rebirth; probably because I have the desire to have been, and the desire to be again in the future-- even if I say I don't, it's subconsciously there.
The concept of rebirth explains to me the things that "need" answering in the world, such as why some people are born rich, some poor, some healthy, some diseased, etc.; it gives "fairness" and "balance" when we look at a world that seems "not fair" and "not balanced". It answers all the why's.
I like the idea, but as I have no proof of it, it could be a whopping load of horse-shit and when I die, my consciousness may just end there and I may become a big wad of dust. That's okay too, because I won't know a thing.
And then my mother may be right, I may end up burning in hell forever for not worshipping Jesus.
I devoted a lot of my thought to Christianity, in my past. For the un-versed in Christianity: We have what's called Pascal's Wager here in the West: Pascal theorized that there are two options; worship Jesus or not. If you do, and it turns out that's the correct answer, you win and gain heaven. If you don't, you burn in hell for eternity. If you do and there's no truth to Christiany, so what, you haven't lost; if you don't, then you still haven't lost. So the best option is to go with Jesus to be on the safe side.
I would wager Pascal's Wager in Buddhism would be better safe than sorry, trust the Dhamma and assume/prepare for the next life, just in case. But I'm not much for Mr. Pascal.
The neat thing about the Dhamma (to me) is that it brings about observable results. If I'm going to practice a religion or philosophy I want to see it giving material/tangible/mental results I can observe. The Dhamma does that. In this lifetime, we see direct results and we see kamma in action. Now whether or not it affects the next life, who knows? I like to think so, but maybe not. If not, who cares? We get results here and now.
I don't think the nonbelief of rebirth is a hindrance to a good buddhist practice. If anything I would consider severe attachment to the belief of rebirth (or the opposite, and severe aversion to the idea) to be a hindrance.