Dismissing an argument for lack of substantive foundation is absolutely an argument for why it is unsound.

Sure, the argument could be unsound, but do note that that doesn't necessitate that the conclusion is also false. That would effectively be an argument from fallacy. Also that isn't exactly what I was trying to say — I was talking about how some people avoid engaging with certain classes of people because they don't think that their arguments are worthy — e.g. flat earthers.

Unfortunately the vast, vast majority of people I have encountered in this vein have had this problem with doubling down when presented with evidence contrary to their belief.

This is indeed an issue. I'm not entirely sure what its cause is. Perhaps it's fear of ridicule, or ostracization? I think the best grassroots method to fix it would be teaching and advocating for proper critical thinking skills.

People living with those kind of delusions, that evidence proving their point wrong doesn’t at least warrant a second look, cannot be reasoned with.

Dealing with irrationality is a tricky thing. How does one reason with someone who is unreasonable? I personally don't think abandoning them is the best solution, but, that being said, I also don't have an alternative.