I don't know if any given religion is right or wrong. I'm an atheist but that doesn't mean I know. I am an atheist because I lack faith. Why don't I call myself agnostic? Because I don't think it matters if I am right or wrong about it.

I agree with Thomas Aquinas that science is inherently biased by our imperfect perception of the world, but don't agree that it's a divine mystery that we are failing to grasp. I would strongly suggest the short story Flatland by Edwin A. Abbott as an illustration of how our perception influences our theories.

I agree with Kant that faith means letting go of logic. And proving something isn't faith. I don't think all religions agree with that though. I know Judism treats faith a little differently than Catholicism, for example. I don't know what the other major religions have to say on this topic.

religion claims to have answers

Is this so? Or do they say, you don't need to understand everything just live according to the rules and have faith? Maybe that's an overall "answer" but I don't think they claim to have answers to every question. My k-12 education was in a roman catholic system. At least that brand of roman catholicism didn't think science was incompatible with faith. It did come up in class though, especially as creationism in the states was coming into the mainstream. The answer was "The bible isn't literal, god created everything, he doesn't object to us trying to understand it, but that's different than faith."

I don't know. In any case, I do sometimes think of a chap I worked with who claimed to be Buddhist, and who said that Buddhists don't believe in god - the way he described it, the world is a mechanical thing, there is no big cheese in control of it all, and karma is not some kind of divine justice being meted out, rather it's just the way the self naturally evolves through time. That viewpoint - of course I may be misremembering it - could possibly be consistent with the "reincarnation" thought experiment of my post.

Sure but like I said Buddhism (in really general terms) doesn't believe in a permanent soul or that reincarnation produces some sameness. They believe that the act of rebirth changes the nature of the consciousness (details vary between sects).

It's important to remember that words like Karma have very different meaning in different religions and sects. Two examples are more of a cause and effect vs justice. Karma as justice is more associated with Hinduism, which believes in a permanent soul. Karma as justice doesn't make sense if you have no soul, right?

I've heard it in various forms - for instance, the somewhat trite idea that "we don't really die until we are forgotten". I'm sorry but once I'm dead, I certainly leave this planet Earth. I will not care if someone thinks of me. The person I am now, that they are thinking of, will no longer exist. That is pretty clear I think. If someone thinks of me now, while I live, it has no effect on my consciousness, it doesn't make me in some way conscious in that person's head alongside them, does it? That's just something going on in another separate consciousness, it doesn't involve me in any real way.

This sounds like a case of you applying your own interpretation to what someone else says. I'm going to talk about the meaning of that phrase because it is in line with what I believe not because I think I can understand perfectly what the person you heard it from said.

I don't mean it literally in that my consciousness lives on if that's how you want to define death.

In my understanding of how the world works, I don't exist to other people unless I am perceived in some way. It doesn't have to be direct and it doesn't have to be real time. I exist to someone who knows the population of my village, province, country etc because I am part of that number. When I die and when the number is updated, I am no longer part of it. I don't exist in that number any more and I don't exist to that person anymore. They don't know all the details, but that doesn't make it less true.

I can perceive being alive and that perception will end with my death (I assume). If people remember me or if my actions are still having an impact on any consciousness they are still perceiving my existence. None of that is not tied to whether I am alive or not, or whether my consciousness is alive or not.

The person I am now, that they are thinking of, will no longer exist.

I don't think anyone can know another person perfectly and the version of ourselves that exists in others heads is a construct. Whether we are alive or dead. The phrase is about our relation to other people not our own consciousness. You have inferred that meaning.