None of us get through life without complicated trade-offs, and in most cases when you disagree with ~50% of a country's population it's because you have different values of what good thing matters most.
Most people are full of contradictions and often carry beliefs that might be seen as controversial (perhaps in hindsight). Maybe it's not appropriate to lump all controversial beliefs into one, but I think a small part of the problem is that we identify ourselves as being morally pure as a way to avoid having hard conversations.
There is a human instinct resolve ambiguity, and barring that, heuristically paper over it.
The more emotionally engaging a topic is, the more galling the uncertainty and cognitive dissonance is. The more distressing the uncertainty, the more people want a simple solution, even if it isnt true.
I think questions like if someone can be a racist AND a good person are complex. They are uncomfortable. This makes a simple answer of "NO" all the more attractive. It makes life a lot easier than if the answer is "sometimes, but it depends on 1,000 other things".
Applying purity tests to others provides an easy way to go through life while minimizing the thought and consideration given to those people.
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So, in some sense it is a "privilege" to not have such a rare and extreme problem.
But, mostly the privilege is in the other direction, and the people with the privilege are the ones who dont have other serious problems in their life that they can afford to spend all their time and effort focusing on something that they have little ability to effect or change and aren't directly related to their immediate problems.
Most the people with material problems are the ones with the less privilege here, even though, yes in some rare cases the inability to avoid focusing on things that are irrelevant to ones day to day and immediate problems can be an issue.
> is life free of that burden.
Quite the opposite. People with actual burdens don't have the time, effort, or luxury to focus on things that are outside of their immediate issues.
They have things to do and problems to solve that are hurting them seriously in the material world.
Its the rich and wealthy, and undiscriminated that have the privilege to be morally pure all the time.