A theme topic, whatever often talked about on this forum, is the $5 hammer attack.
Many people suggest to keep your bitcoin holdings secret, thus preserving the anonymity of bitcoin to a certain degree.
But then you get sportsbooks asking for photos and passports, and god only knows what else.
If a sportsbook wants all this, I respectly suggest they change to fiat.
If you don't want to give the details then simply change the site you are playing and I think not all the gambling sites were asking for KYC to complete because all they are doing is paying the rewards even in crypto so they might save them from legal actions with the same anonimity you are talking about.
This is very easy to understand if you should go for KYC. If you do not worry about your identity and want to avail those few dollars, you should not stop and enjoy and go easy with KYC. However, if you do not have another option and you do not want to share your details, just leave the site and look for another with not restriction about the KYC. Simple is that.