Which AV packages fully support those browsers? The big AV companies support Microsoft, Firefox and Google Chrome - just checked Norton and Kaspersky. Many of the other browsers don't have full support or current support. Getting caught out can be really unpleasant. Just ask the DNC or the Clinton Campaign - lol
I believe PaleMoon is treated by many AVs as Firefox. You can always install an add-on to integrate your AV to PaleMoon, for example Fireclam.

There are a couple of link checkers for Opera, but no integration. You have to set-up your AV to scan downloads automatically.
Support? Any good AV package should be able to protect your computer without having to support your browser. In fact, most AV browser "support" is stuff like this.

The only real issues are tracking, spying scripts, spoofing sites, and security flaws in the browser. And the threat from these can be managed through proper considerations and common sense.
Ayye if ur finding a anti virus software u NEED MalWarebytes. It's the best
@Zolxys Yeah, I completely agree. I get rid of these things immediately. If I download something funny the AV finds it anyways, so what's the point. I use uMatrix, so there's no funny business with website scripts either.