I guess your point is that spreading disease is something Health Departments want to avoid.
I imagine that it is fair to say that many Gays and Lesbians have Sexually acquired diseases (AIDS, herpes, etc).
Most in the gay parades seem to be clothing challenged. So if this or any other place said “no shirt no shoes” they are abiding by the Health Department codes and may turn away people for this reason. Would hope the police would enforce laws against public nudity as well seeing that is a food place.