Most religions have the idea that it’s different to take a life than to stand by and do nothing. For instance, you should always try to help others (save a life), pretty much above all else. However, to take a life, requires taking action. Ie standing by as someone drowns is not the same as sticking someone under water. For murder you’re damned to hell. For standing by you’ll need to repent, but it’s a lesser sin.
The trolly problem IMO is a framing problem. (1) it assumes you know the future and (2) it assumes your will is above others.
The example I typically gave people when discussing this problem is actually in this fun exercise. Imagine if the 5 people strapped themselves to the tracks. Imagine they knew they would murder and wanted to die rather than murder. When you redirect the train, you actually cause more deaths, because you didn’t know the intent of those people.
The exercise helps you decide what you value. For me I never apply my outside influence to the system, except when I can save a life without costing a life. I believe life is more valuable than pretty much anything I saw in the game.
I’m a realist and objectivist. So for me the question is “what could I live with?” And “what information do I have to make a decision?”
In reality, everyone in this situation made their bed (so to speak). So I am unwilling to ever impose my will into the system baring saving a life (without costing one).