The Church of England is the "established church" in that country. That is, it is instituted by law as the official state church. Over the years, some people came to the conclusion that it should not be 'established' in this way...ie they wanted 'disestablishment'. As a result, they were known as 'disestablishmentarians' and their belief was labelled as 'disestablishmentarianism'. Of course, an opposition group set themselves up and just guess what they were called...that's right...the 'antidisestablishmentarians' and their belief was labelled as 'antidisestablishmentarianism'.
I would say because they were against the people who were antidistrictofcolumbians, not against antidistinctlyminty itself. BTW Quizmonster you never cease to amaze me....
I quite agree about the double negative, Obo, but I imagine they felt the 'anti' prefix somehow had more oomph about it than just the basic 'est...' word. That is, they were saying: "We're really against you 'dis...' folks!"
establishmentarians would be those who want to establish a state religion - which we already have, so the double negative is justified - though you could say pro-establishmentarians, I suppose.