Aside from the homophobia, Brave also runs an ad network so I’m skeptical about their privacy claims.

Brave was found altering links to some crypto services like Binance to include their referral and basically profit from unknowing users, they also run an ad network, they rely on Chromium, thereby endorsing Google's dominance over the modern Web, they are very crypto-positive, which is a problem for many in the open-source community, and on top of that, everything else others have said.

Their very shady history + their very bigoted owner + current shady tactics

Edit: and on top of that it's Chromium based

They do a ton of sketchy shit. I was skeptical, but this article convinced me.

If you need to use a Chromium browser, there are a shit-ton that aren't Brave. I use Ungoogled Chromium.

Brendan Eich. Specifically his stance against same sex marriage. He was pressured to resign from Mozilla, which he cofounded, due to his support of California's prop 8. Then he founded Brave. The Brave browser also has some annoying crypto and AI features turned on by default. I think it's a perfectly fine piece of software. I use it as a second browser.

I don't want to use a web browser maintained by the guy responsible for our JavaScript hell

The guy who made it has bad beliefs. It's good software from what I can tell, and free as in speech and free as in beer, but if you use it you get his bad bigot cooties. You have to use free software by certified free range organic non-bigots or it rubs off on you I guess.