Conservatism doesn’t support the current system which happens to be oppressive, they support the current system because it’s oppressive. The original Conservatives formed because they wanted to defend the monarchy, which was a system of oppression which makes even capitalism look tame by comparison. The only reason they jumped ship is because socialism became the greater threat.
As for the ties to child abuse that’s a case of just look at the connections and the people they choose to align with.