In his insightful book "The Smoke of Satan" Phil Lawler discusses the scandal of child abuse that was done by Catholic clergy (mostly in the last century) and points out the consequences of it that are not always known. What he also points out, that not many people see, is that a priest who is willing to commit such horrible sins was already committing a sin that is (in more than one way) worse than child abuse; and thus, it leads to sins like child abuse.
For priests this starts with the sin of spiritual compromise, then leads to liturgical abuse, and then opens the door to many other kinds of abuse of God's people. The heart that is already twisted, will simply head down the road of sodomy, ephebophilia, and pedophilia (which is actually a rare perversion in abusive priests). It is a point that I have made before. If a priest is willing to abuse the liturgy of the Mass and show contempt toward God Almighty, then it should not surprise anyone that he will eventually be willing to abuse people as well (even some of the most vulnerable).
For all of us, the stain of perverted priests hurts deeply. Yet, if my (and Lawler's) assessment is correct, then we cannot think that we are now ok if we have accomplished means to prevent priests from hurting children. After all, if liturgical abuse "opens the door" to other things, then we must realize that we have only stopped one symptom of people hating God, but not stopped that actual hatred that causes them to abuse the liturgy. The devil can be tricky, and if he is doing a good job of encouraging liturgical abuse, then he will only direct the wicked hearts of those who do this in another direction (and it could be far worse than child abuse!).
You cannot make an ugly building go away by closing your eyes. You cannot heal a broken arm with a pain killer. And, in the same way, you cannot stop evil from happening by putting up a big fence (you only make it happen somewhere else!). We need to stop the liturgical abuse. It does not matter if it is Novus Ordo, Latin Mass, an Eastern Liturgy, or Divine Worship. If it is supposed to honor Christ, then the devil will want it abused as an easy means of leading to other evils. Watch the symptoms, yes, but make sure that we are fighting the actual disease.