Here's some research: https://www.ncbi.nlm.nih.gov/pubmed/18555116

In short, only a few religions have anything to say against being a donor at death, and a few have something against being a recipient from a dead person.

If you think your religion might affect your decision to be a donor, check with a trusted authority figure and make sure.

For sure, FWIW I'm personally an organ donor and broadly agree with your logic. Those are just some times when I feel the choice not to donate organs is valid.

A person's choice is probably always valid regardless of what it is, it's their body at the end of the day. In the normative sense I think everyone should donate their organs, but I'm not sure it can be reasonably codified.

If your religion forbids saving or improving the lives of others with organs you're done with, please consider alternatives.

Religion doesn't work that way. You don't go "Well, I have this set of values, so I think XYZ is the right religion for me". There are exceptions, but most of the time it's actually exactly the opposite.

If one facet of someone's faith is enough for you to dismiss their entire belief system, you clearly don't even try to understand others' differences to yourself...

Oh, I try. But in the case of organ donation, I simply fail to understand the reasoning. If you're dead, why not save a life, renew sight, or otherwise greatly improve the life of another? Are there people who think that organ donation would hurt them in an afterlife? We, at least in the first world, live in societies with freedom of conscience and belief, so people should at least think through the consequences of their choices on others. (And on themselves; if there's an afterlife, do you really want to risk being judged on the basis of having chosen to deny a chance at health and wellbeing to another person?)