I don't know what show this is from, but that's an awfully strange choice of words to use to describe your butler, and I'm just saying this wouldn't be the first time Tumblr has lied to me about what the dialogue in a TV scene was.
This is from The Nanny, but I don't know the episode. Those are the two main characters, though Fran is in a blond wig for some reason. It was made in the 90s and not in black and white, so this must have been a strange episode.
It's a play on words assuming that you know both meanings of all 3 words, which the audience clearly did.
Also, it was during a time when people were becoming more aware of queer rights and those words were becoming offensive to more Americans, part of the joke, kinda like "you should never say this in the US, but in the UK it's totally acceptable because all the words have different meanings than in the US"
It's also a play on linguistic drift as mentioned in another post. It's also hanging a lantern on how unacceptable that kind of language had become and in that sense was progressive.
I cannot think of a way that joke flies in the US today unless in a meta context of old jokes, which this meme attempts.
Hopefully this explanation has made the joke completely unfunny at this point.