There’s no real way to do it. Unless you know someone who can trade you XMR<->cash and you somehow convince your employer to (break laws and) pay you in those forms, you can’t avoid it. At some point, you’ll have to get money on a real bank account, which requires real information to open.
As far as I know, modern cards don’t just send your CC info to terminals, they do some form of a cryptographic handshake (probably a pubkey signature or similar) which gets confirmed by your bank. I believe Caveman was talking more about online shopping, where you have to enter your card number, expiration date, CVC and often your name too.
Adding onto what’s already on the thread, you can try look at the newer Element Call, which is an implementation of Matrix’s native calls.
I’ve been using it a bit recently, since Jitsi seems to have stopped working reliably for me (to be frank, I’ve not put much effort into debugging it yet). It works well, but it’s still early stage, lacking some features Jitsi has. If that one works for you, I recommend you stick to it.