Antidisestablishmentarianism itself refers to the opposition to the separation of church and state, specifically in the context of the Church of England. It's a very long and uncommon word, making it a fun target for wordplay.
The addition of "pseudo" implies a false or pretended form of antidisestablishmentarianism. This makes the word a humorous exaggeration of the already complex concept.
Essentially, "pseudoantidisestablishmentarianism" is a made-up word used for comedic effect and doesn't hold any actual meaning.