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.
It is true that most people have shared their KYC with several exchanges, or other platforms that require KYC. However, i think there are people who choose on which platform they will do KYC, or not at all. I think everyone has the right to do KYC or not, with all the consequences. It all comes down to preference, and i agree with you that there should be no problem doing KYC, especially for sites that are trusted enough, and well-known sites are usually relatively safe, especially those related to this forum.
So you've done it all.
KYC is now mandatory because some platforms already have some rules that must follow government directives, so it is difficult to avoid it.