I think the OP pertains to the anonymity of one's legal and personal information more specifically a user's submission to a gambling's KYC. Knowing your IP isn't that an "anonymity" killer, but just a vulnerability, and gambling platforms that bypasses its user's security is often red-tagged.
Knowing your real IP without also knowing any other personal information doesn't make you anonymous though, does it?
You're automatically giving up your real IP and an e-mail address you own upon registering; KYC makes it so that you also
willingly give up other critical information of yours in order to be accepted on the website (or in order to extend some features of your account).
Just think about it: you use the same IP to register 2 accounts under the same e-mail, out of which one is supposedly "anonymous" and the other is an exchange you've completed KYC on. As soon as the KYC is complete, you literally fully de-anonymize yourself on the former account. Not to mention other fingerprints you leave behind, including but not limited to the way you write, your English skills, your browser fingerprint, your activity (part of which is tracked on a large part of the currently existing websites) etc. If IP wasn't an issue, Tor Browser, Tails, Qubes etc wouldn't exist.
So if we want anonymity, we should start studying this stuff from zero instead of jumping in the misleading "crypto anonymizes your accounts" train. First and foremost, the biggest flaw in this argument is that you literally automatically give up enough information to be identified by a bad actor (incuding the state) when
visiting a website.
A good potential solution to all of the above might be launching a crypto gambling website on an Onion link that has no JS requirement and allows Mail2Tor registration. But that would completely kill off the fun as no JS means no more fast-paced gambling. For sports betting however, it might not be a problem - so that could even turn into a combination of JS-required gambling (blackjack, dice etc) and a no-JS part of the website that allows bet placing for sports gambling. Biggest issue here is that only very few are looking for privacy to the extremes, so not sure how successful a such website would really be.