There will be no problem.
Most people have submitted their KYC to centralized exchanges, to bounty projects, to companies who open job vacancy etc. People already have zero privacy, so what are they afraid of?
People who care with KYC and want to stay anonymous at all cost is really small, even Bitcoin is popular with the pseudonymous, but probably only 1%-5% is really care with their privacy.
This is common requirements ask now and for sure those old timer on crypto space already know about this implementation and majority for sure will not see it as big deal especially if the casino is well known reputable platform.
Being anonymous is not a main concern of people now since what people looking for is those safe casino on where they can trust there funds or even they have chance to withdraw huge amount of money if they win big prizes with them.
Few people now pay attention about it and usually they are skeptical to provide that requirements if the casino is new.