Now, I will say this is not necessarily a discussion limited to English speaking parties. I know Japanese Zen priests who by their own admission deny rebirth. On Japanese forums likewise I see a lot of denial. My opinion is that modern Japan is actually by default materialist.
So, basically, this kind of denial exists outside western variations of Buddhism as well.
Now, the one thing I wonder is what the effect of this will be. Materialism, which denies the possibility of rebirth of an individual, is evidently influencing Buddhists. You can have people saying, "I'm a Buddhist, but I don't believe in rebirth."
I think this is really just the default mentality of most modern day societies dictating the direction a person will take in their beliefs. Even if you're "religious", you're likely to possess a materialist reality-world picture owing to the fact that your society and education officially sees such a picture as the most real and appropriate to hold. Rebirth is a belief. Post-mortem oblivion is a fact.
But if you really think that at death you become nothing and thus there will be no experience of anything at all ever again, that also means you will not be subject to the consequences of the life you lived. In short, if there is just oblivion at death, then whether you cultivate saintliness or just indulge in material pleasures all day long is irrelevant because the end result is the same: nothingness.
I mean even in ancient India there were materialists who had the same idea. Take for example this quote from the Sarva-darsana-samgraha:
That the pleasure arising to man
from contact with sensible objects,
is to be relinquished because accompanied by pain—
such is the reasoning of fools.
The kernels of the paddy, rich with finest white grains,
What man, seeking his own true interest,
would fling them away
because of a covering of husk and dust?
While life remains, let a man live happily,
let him feed on butter though he runs in debt;
When once the body becomes ashes,
how can it ever return again?
So, as they say, just live it up as you only live once.
But from the Buddhist perspective you're actually accountable for your actions post-mortem. You will experience the results of your actions in future lives. Just as you plan for your retirement not wanting to live poorly in the future to come, so to one plans for future lives and makes proper plans and refrains from doing anything that would jeopardize future well being. You wouldn't take all your life savings and toss them away at the casino in an afternoon. Likewise from the Buddhist perspective you wouldn't jeopardize your ability to cultivate yourself in future lives. You need to retain the ability to cultivate yourself towards liberation. The only other alternative is samsara and that is unacceptable.
But if all there is is nothingness at death, whether you lead a moral life or immoral life is irrelevant. I'm not proposing all materialists are immoral, but merely that with such a view in mind there really is no actual real vested interest for oneself in morality. Immoral or moral, the result is the same and any potential consequences from either course of action is the same: oblivion.
Without rebirth the whole system of Buddhist ethics falls apart. This is one reason why I cannot accept "Buddhist thought" that would reject rebirth. There is no Buddhism without rebirth. The whole idea of liberation is predicated on the idea of cyclic existence from which one must find liberation from.
If actual morality is tossed out the window, then the Buddhist systems that will emerge will be inherently unstable and subject to rapid decay. Buddhism in many places could quickly fade away if the necessity of real morality is quietly set aside. I'm actually witnessing this here in Japan. Japanese Buddhism in general is rapidly in decay owing to the fact that morality and ethics are treated quite softly and often ignored.
Thus why I think we really need to stress rebirth and system of ethics predicated on rebirth if we are to see the Buddhadharma continue to exist in this world.