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?
"There is a Catskill eagle in some souls that can alike dive down into the blackest gorges, and soar out of them again and become invisible in the sunny spaces... even in his lowest swoop the mountain eagle is still higher than other birds upon the plain, even though they soar." -- from Moby-Dick