Often these are ideas that I don't agree with, but I can't articulate exactly why I disagree.
When I argue it, I can get others to argue against the idea, and so I can discover points that I may not have been able to put to words.
It's essentially idea farming.
Their followers might not even believe it but still support and spread the argument, for their own selfish reasons.
Say Hitler pronouncing that Jews are an inferior race worthy of destroying. Did his followers really believe that when they agreed with him, or did it just seem in their self-interest to spread such propaganda further, and seize the property of Jews?
Just an example from past but I believe similar examples happen all the time. Some people argue in bad faith. If that is the case there is no reason to argue with them.
You kind of have to. If you were not emotionally invested in some way, you wouldn’t be arguing.