There is very little true pedophilia in the Church. It is much lower than in virtually any trade or profession. Also it is significantly lower in the Catholic Church than in any other Christian denomination. Many, many more instances occurs in the more ‘liberal’ Churches as well in the LDS and certainly the Muslim religions.
That being said. The effect of the Homosexual Lobby in the Catholic Hierarchy of the Church, often called the Lavender Mafia, can not be over stated. It has brought great disrepute and done great damage to the Latin Church. It is almost certainly be caused by the loosening of the acceptance standards for homosexuals into the priesthood. The Homosexuals than rapidly advanced and often filled very influential posts in the hierarchy where they could protect and cover for their and their fellow perverts.
Make no mistake. The Liberals in society have no real problem with Gay Priests as they approve very much the same activity in the wider secular World. They also appreciate the opportunity to bash the Church of Rome since they hate any organization that willfully stands in their way of sexual and secular utopia.
Historically this has been the "normal" type of homosexuality. See ancient Greece, Japan, China, Afghanistan, etc. Today's "consenting adults" meme is the anomaly.
BTW, good luck convincing anybody that pedophilia does not refer to attraction towards any person (arbitrarily) defined as being under the legal age of consent.