I also refuse to use anything from Brave for this reason.
This is not about separating a person's work from their political views, it's about not giving more power to people you don't want to have more power. If he is going to use money to campaign against LGBT people, then I'll do my best not to give him money, and I think you should too.
It's not that hard to prioritize companies that are aligned with your values. You don't need to start living in a cave or self-flagellate. Just look around to see if there is a suitable alternative.
Then yes, I use Google for my search engine. They do shady stuff, but they never campaigned against same-sex marriage, and none of the alternatives have given me good enough results and an acceptable political alignment for me to switch. Brave certainly doesn't seem much better, with unacceptable political stances and worse search results. DDG is getting there, but the search results are still not good enough to replace Google for me.