My grandad donated his body to medical science.
For me the difficult part has been dealing with his absence in my life, not what happened to his body after he died. We got ashes, and we've had ceremonies etc, just as we would have done without his donation.
The only real difference was that we had the interment a year after his death because we had to wait to receive the ashes back. In some ways though, it was lovely, because it was a ceremony filled with real joy and love - we had all gone past the immediate grief and there were almost no tears at the ceremony, just a lot of loving memories and laughter.
He was a wonderful man and I adored him, and I love to think that his final wonderful act was to help others, either a doctor learn, or science as a whole learn something new.
He couldn't have been an organ donator but the idea that other families may have had futures together because of him would have been equally amazing.
Someone said upthread that there would be grieving families either way. Without organ donation, there may be 7 or 8 grieving families, having lost children, aunts, dads etc. With organ donation, it's just one. It's one too many and it's no less hideous for them, but many people could be spared the grief.
I'm not religious. I don't believe in any kind of afterlife. I believe what we have here and now is all we have. It's absolutely amazing, this thing called life, but it's fragile, and we all only get one very brief shot at it. So my belief is everyone deserves the best shot possible. And so you need to be kind to others etc, not because you are laying foundations for a great afterlife, but because you are trying to give everyone a chance to have a great life. And as organ donation is possible, then it's one way of making sure that someone else can carry on having their shot at life when mine is over. Because otherwise my organs will just be cremated and go to waste, I won't know or care anyway, and others will also lose out on their chance.
The thing is feelings are feelings and not always rational. Everyone is well wit hint their rights to feel weird. It's what you do next that counts, and deciding it's irrational and trying to explore those feelings that is a very brave step.