If you us Mullvad browser, which has built in Mullvad proxies, this isn't an issue because it doesn't use wireguard.
The browser also has a cool feature in the browser extension called Random mode. This gives you a different IP for each site, improving your privacy.
You can probably also use it on regular Firefox.
Which you absolutely shouldn't use, because just like Tor Browser before, a vulnerability in the browser can be immediately escalated into decloaking your real IP. Ideally the proxying doesn't even happen on the same machine.