To be more clear and direct,
Yes you are correct. Some sites may ban you if they find out you are a sex offender but that seems to be dying out except for dating sites.
Whatever you do, DO NOT hide you name when you sign up. I am NOT talking about your screen name. That can be whatever. When they ask for your name when you sign up, if you lie, that could get you into trouble as you are trying to hide the fact you are a sex offender they could claim. 99.99% This won’t matter, but if there ever was a dust up concerning you and one of the site you belong to.
I personally on certain sites that “officially” do not allow sex offenders, but as long as you are not doing or saying things you shouldn’t be doing, you will be ok. I do know all major dating sites will not allow sex offenders on and yes they run registry checks.