I hear you. Part of the confusion has to do with UK politics and that "liberal" and "conservative" mean slightly different things there as they do in the US.
2ndly, while liberals are certainly capable of being pedos and involved in pedo rings, there's a certain sort of pedo that is also militant and hypocritical on an extraordinary level -- so outwardly and publicly "conservative" while secretly decadent and predatory.
Does that help?
But he grew old, this knight so bold / And upon his heart a shadow / Fell as he found no spot on the ground / That looked like El Dorado.