No tradition, except maybe Secular Buddhism, rejects literal rebirth, it is a core part of the dhamma. I will say though that there is evidence the Buddha was never " believe in rebirth or else."
Probably the most famous Sutta for Western Buddhism is also the most over rated, misquoted and misunderstood. That being the Kalama Sutta. It is most famous for its paragraph talking about not going by reports or because someone says something.
What is much more profound, and more important imo, is the lesser known section towards the bottom of the sutta, where the Buddha says... ok what IF there is no rebirth and kamma..
Kalama Sutta: To the Kalamas
"So it is, Blessed One. So it is, O One Well-gone. One who is a
disciple of the noble ones — his mind thus free from hostility, free
from ill will, undefiled, & pure — acquires four assurances in the
"'If there is a world after death, if there is the fruit of actions
rightly & wrongly done, then this is the basis by which, with the
break-up of the body, after death, I will reappear in a good
destination, the heavenly world.' This is the first assurance he
"'But if there is no world after death, if there is no fruit of actions rightly & wrongly done, then here in the present life I look
after myself with ease — free from hostility, free from ill will, free
from trouble.' This is the second assurance he acquires."
Now does the Buddha in multiple places basically say that believing there is no next world, no fruit, etc, is wrong view? yes he does, but as you can see he is never " thou shalt believe in rebirth... or else!" He is much more focused on your practice here and now bringing benefits and teaches to the level of the person, from basic generosity and giving up to kamma. I think that western people today get really hung up on intellectual pondering regarding topics like rebirth when they should be practicing, here and now is the most important place and time, in this precious human birth, where we can practice dhamma and free ourselves.
As far as a quick personal addition to this if I am allowed. I am a practicing Buddhist, have been for 6 years. I'm also close to getting on the path to renunciation and becoming a monk. I cannot say I BELIEVE in rebirth and that has never been a hindrance to me in Theravada. No monk has scolded me,judged me, or held me back in any way.
I am an agnostic and keep an open mind. I have also through my practice proven the Buddha to be dead on accurate about many things, so at this point I have enough confidence and faith in the dhamma to say "hmm.. if the Buddha was right about all this.. why not that?".