Has there ever been a sitcom with homosexual characters or homosexual themes that has succeeded?
"Will & Grace" comes to mind.
Soap.
Modern Family.
Which BTW is AWFUL.
I think "Will and Grace" was considered successful, and I am told that one of it's main characters is a homosexual, but I don't know for sure, i've never watched a bit of it.
"Are you being served" was a British sitcom (from the 1970s) that lightly touched on the subject and featured a prominent character who was portrayed as probably homosexual. It was an ongoing bit of humor for them to speculate whether "Mr Humphries" was really "gay" or just effeminate.