Specifically, WebRTC leaks two bits of info that may compromise your privacy:
Device ID hashes for your microphone & camera
The IP address on your local network
#1 can be used for browser fingerprinting, allowing the likes of Google and Facebook to secretly track your online activities; luckily it's mostly a problem for Chromium-family browsers, not for Firefox-family browsers like Basilisk. The latter browsers randomize the "salt" used in the hash whenever the browser is started, so unless you leave your browser session running for weeks at a time, the ability of anyone to use #1 as a secret tracking cookie is limited.
#2 is more problematic though. It can reveal your "real" address behind a VPN, which could be used for censorship, or alert the authorities that you're accessing "banned" material. More commonly, it will reveal one of those non-routeable local IP addresses starting with 10. or 192.168 assigned by your (real or virtual) router. That's less worrisome, but if it doesn't change often, it too can be used in conjunction with your public IP for browser fingerprinting.
If you don't need/use WebRTC, the website linked above contains instructions for disabling it and preventing those info leaks. But what if you do use it?
One solution might be the WebRTC Control add-on. This adds a toolbar button that simply toggles WebRTC on or off, a la the popular Flash Disable add-on. So you can leave it off for normal browsing, but turn it on before going to a site that requires it.
Edit: Should have checked first. Couldn't install WebRTC Control linked above. All three versions download OK but Basilisk reports that they all appear to be corrupt. Must be a bad hash somewhere Try the "classic" version of Disable WebRTC instead.
I think a better solution would be an add-on with a white-list, which would enable WebRTC automatically, but only for sites like Discord and Skype. But I haven't yet found a Basilisk-compatible add-on that has such a white-list