I can't answer that for sure, but I think not. At least not in my area. Also, where I live in the US, it is extremely difficult to have visitation taken away from a parent. You may disagree with his religious beliefs, but he has a right to practice it. Now the sexual offender friend is interesting, you need to keep any contact well document. Still, if you can't prove the children are in danger, he will get to see them. Even if you do prove they are in danger, he will get to see them under supervision until he convinces the court he is no longer a danger. Then it's back to normal.
I know it's frustrating--we want the best for our kids. But a born-again christian might think it's unhealthy for the children to be with their catholic parent and viseversa. Also, just not showing up for visits is a frustration many parents deal with, but again, they end up just having to deal with it.
I may have missed some details, and I'm not a lawyer, but I've found myself needing to research these things for several reasons. However it may all be unique to the area I live in. Different court systems have different standards. My ex tried to bring up religion when going for custody. The judge cut him short and said that was not a consideration he would take up in his decision.
It's a really big deal to cut a parent's rights. Only the most extreme circumstances accomplishes it. You wouldn't want your children to experience the extreme circumstances. In one case of proven abuse,a parent I know was only able to limit visitation to supervised visitation. When the ex fullfilled all of the required classes and therapy, visitation was reinstitued.
NC