What affected me for a long time, and therefore meant I was reluctant to donate, are the tests used to determine death. Because, the person is on life support and you have a doctor in front of you telling you that person is dead when to all appearances they don't look it.
Apparently the death of the brain stem is the key factor. But I am sure I have come across at least one report that a person has made a recovery after the brain stem was tested and they were declared dead. I also saw a report that some doctors are querying whether testing the brain stem is actually the right way to determine death.
I have also struggled with the reports that anaesthetics are used when harvesting the organs. If a person is dead, do they need these?
And don't forget the influence that popular fiction has on people. There are many novels, tv programmes, films, etc, that in one form or another have featured the idea of someone being wrongly declared dead and who may or may not escape the peril of being killed for real.
I think donor reluctance is the modern equivalent of being buried alive, it's the question of "is this person really dead?".
And that is probably a big reason behind a lot of donor reluctance. It certainly affect me, but I'm happy to donate if the time comes.