I used metamask (the same wallet) on all of them and I never had any problems with that! I used and I am using other extensions for some other coins as well, without any problems! Not just metamask for ETH, I have TronLink and Binance Wallet! I experimented with different browsers and all these wallets work perfectly fine for me on each browser!

I think we Firefox, Brave, and Chrome are ok, and I am sure they will be ok, but whoever seeks extra protections should use VPN first, maybe even TOR browser, but just for people who wish to be extra careful, if they have a good reason for that!