Except the proportion of paedophile priests is about the same as the proportion of paedophiles in the general population. There are more paedophiles in schools and social services than in religious organisations - and there have even been more convictions of teachers and social workers, at least tin the UK. The reason you think of the Catholic Church this way is BECAUSE it got more media attention earlier than elsewhere. A surprising number of people the UK do not know about the biggest big paedophile scandal in the country, the Islington one, that was huge, and at least one politician who was responsible for the failure to investigate went on to have a successful career in politics (the only time it set back her career at all was when Blair wanted to make her minister for children there was a backlash)

If you posit a conspiracy that only involves a few people who could plausibly coordinate to conceal the truth, that's also not a grand conspiracy, and we don't call people conspiracy theorist for believing in regular, everyday criminal conspiracies.