Democracy is about submission of the minority. To believe in democracy means to believe that when you are in the minority, you must submit to things you disagree with. There is grey area around human rights and bad faith legislation/corruption.
If I don't trust the election, that means I don't believe I'm actually in the minority, and if I don't believe I am in the minority, then I am being subjugated and oppressed by people who are using power to get their way rather than a mandate from the people to execute the people's will.
I am extremely liberal and Trump is the avatar of everything that I hate, but I don't believe the election is legitimate either. A sitting president called an election official to sway the election, and 2 years later it's not clear there are going to be any consequences. The mechanics of mail in ballots was messed with during an election cycle, and the person who did that is still in control of the postal system. If there are no timely consequences for attempting to cheat, how can you trust the integrity of the system? I don't. There are clearly no checks and balances for actual and obvious attempts to manipulate elections.
I think you can talk to just about anyone who works in security and they will tell you there is no reason to trust voting machines. On slashdot, the technical community nearly universally said "this is a bad idea" when Diebold voting machines were first adopted. That sentiment has been strong through technical communities for a long time. Even today, I think if you asked HN "from a technical point of view are voting machines a good idea?" there would be a resounding, absolutely not.
Because we won, it's less of an issue for us, but had we lost, we would question the results too. We would look around us and experience that no one else liked trump and ask "how can these results be legitimate" too, the same way they look at the people around them and go "everyone liked trump, how can these results be legitimate?" He called a Georgian election official, are we sure that didn't work? Did he call other state's officials and we didn't hear about it because it did work? How do we know? How do we know Biden didn't do that?
Denial is the first stage of grief.
> people have shown that they will not believe in the validity of the election regardless of the evidence presented.
You are failing to have empathy for these people. Evidence cannot be presented, because the mechanics of elections are not able to produce evidence. I am a well educated US citizen, but I think our elections amount to "trust us." Of course people don't believe evidence presented, because the evidence amounts to "trust us." "Trust this extremely complex system that only a handful of people might know how it functions in depth."
You say "regardless of evidence presented," but what if the system is not actually capable of producing satisfying evidence? What if the evidence is actually not satisfying? What if there were systems that could be satisfying, bit this one isn't able to be?
In Taiwan I could go watch an election and I found the legitimacy of it to be self evident because I found the mechanics of it simple and hard to argue with. I don't think there is anything self-evident about our elections. In America, who runs the voting machines is an important question. In Taiwan, who facilitates the voting stations doesn't make much difference. "Are the voting stations being watched" is an important question in Taiwan. "Are the voting stations being watched" doesn't really make sense here since we have mail in ballots and other methods.
Taiwanese don't have to say "trust us" they can say "go watch the election happen."
A hard pill to swallow for most of liberal America is that conservatives can be right for very wrong reasons. It's easy to say "you don't think the results are legitimate because you lost," it's much harder to say "can somebody in good faith not trust the election results?" "what might we have done to decrease trust in elections?" "Can we make our election system more resistant to claims of bad faith?"