When logging into the website on a device that is using iCloud Private Relay, it
successfully
logs in but then returns to the login screen.
I don’t have this sort of incompatibility on any other sites I visit and log into. It also only began to be an issue recently for VRChat’s website.
iCloud Private Relay is in part run by CloudFlare. A company whose services you use, I believe. So I would assume it would be compatible with your security.
Being forced to lower privacy protections to continue to use the website would be a huge bummer.