I recently had a bit of a run-in with the administration of a large Buddhist internet forum. The administration had recently changed and the new powers were taking a dim view of the free-form expression and allegedly almost 'anything goes' attitude of many of the posters on the Zen forum and were taking steps to purge this element. References to burning Buddha statues, killing the Buddha or questioning the authority of the mainstream interpretation of Buddha's teachings were to be forbidden.
Now, I've never been much into posting pictures of flowers or *gasp* pop lyrics on that forum. Most of my involvement was relatively serious discussion. Nor have I seriously challenged the accepted view of the content of what Buddha taught. However, I freely express my own agnosticism or doubt about unknown metaphysical truths such as the traditional descriptions of karma and rebirth.
Because of not accepting this, I thought I would have to always remain on the periphery of Buddhism. Yet it is clear that the Soto Zen sect I belong to does not insist on such beliefs. It appears that Brad Warner's branch of Zen does not insist on such acceptance or belief either since when I asked Gudo Nishijima directly about the afterlife he replied essentially that when we die 'that's it'. This as far as I understand could actually be classed as the view of Annihilationism - definitely regarded by Buddha as a 'wrong view' but this is another story and perhaps I misunderstood him.
Even though these administrators were not Zen practitioners they took the view that 'Zen Buddhists are Buddhists first' - in the sense that Zen Buddhists too had to accept 'Right Understanding' and that Right Understanding included acceptance of karma and rebirth.
My take was that a Zen practitioner does not cling to beliefs one way or the other. That moment-to-moment rebirth renders life-after-death meaningless and that belief that 'we' will be reborn ('sans self' or not) may be a form of covert Eternalism. But it was made clear to me that my views were not welcome anywhere on the board, so I have voluntarily avoided the place since.