Is belief a predicate for salvation? In a Buddhist (and Hindu) sense, must one step aboard the karmic treadmill in order to achieve enlightenment, or can one munch upon a doughnut on the sidelines and still, somehow, be elevated to a state of having been saved? — Buxtebuddha
Keep in mind that in Indian religion, it is precisely the karmic treadmill, known as samsara, that one endeavors to liberate oneself from. Having any sort of karma, even good karma, is in the end a hindrance to liberation. This is why before the Buddha departed the world, he had burned away all his remaining karma. He didn't die, since death is the result of karmic processes. This is the goal of the Jain ascetics who practice sallekhana as well. I may have misunderstood the meaning of your metaphor here, though.
That being said, there are means to aid one's salvation in Indian religion that operate according to something like grace, and so only require sincere belief. In Hinduism, the various gods and their avatars perform this function. In Buddhism, the celestial bodhisattvas, especially Amitabha, can assist one with their superabundant good karma. All one need do is believe and chant his name. They retain and store this good karma because they have staved off parinirvana and choose to stay in samsara until all sentient beings are liberated.
Even within human interaction, is belief in another's potential to be saved when they themselves do not believe in salvation, enough for them to be saved? — Buxtebuddha
I don't think we have that kind of power.
In a way I think the Christian God may be similar, in that he believes in his salvation being able to believe in themselves, and as a result, him as well. — Buxtebuddha
Do you mean to say the Christian God believes that humans will be saved? I think it's rather that he desires this. God doesn't have beliefs, but he does have desires, one of which is that all will be saved. Because desiring something doesn't make it so, however, the possibility of hell (that not all will be saved) remains open. This is similar to your desiring the good for your friend. The mere desire alone has no efficacy with respect to her becoming a better person or what have you. That's entirely up to her.
Yet, it would seem that if one does not believe in the Christian God, you won't be saved. — Buxtebuddha
What matters, of course, is what God thinks it means. Within Christianity, I would say this means trusting in who Jesus allegedly is and has done.