Doctor's don't need to consciously change their behavior for there to be a difference in care. It's just that incentives are like really awesomely powerful things.
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.
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.
Because I have fundamental issues with the economics of organ donation. I do not want my organs used in million-dollar surgeries to save elderly rich people. I would much rather that money be spent more efficiently on younger/poorer people where it can save more lives. How many flu shots could be purchased for the cost of one heart transplant? I cannot change the economic realities of modern medicine, but the least I can do is not contribute my own flesh towards the problem.
I wish I had recorded something I saw at the gym years ago. An old and obviously ill man was bragging about how his firm could hire young interns, pay them nothing, and fire them at the drop of a hat. A young man overheard, walked over to him and said "I;ll never have your money or power, I cannot stop you from being a jerk, but when your liver starts failing you aren't getting even a piece of mine." He then ripped up his organ donation card.
Do you have a source for this? To me, it seems extraordinary that we're capped out of medical resources in such a way that, were someone to not have donated their organs, ~10k flu shots would be provided instead of the various potential transplants. (I tried some internet searching but everything talking about resource constraints was talking about the organs themselves, not the general medical resources).
Also, technically there is no difference between cannibalism and organ transplants - ingesting the flesh of others of your species to save your life.