It would be no different than another person saying I am a "Pro-God Atheist!" Unless one is living in a world of their own, they have to agree that such a label is an intellectual impossibility. A person cannot deny the existence of God, while at the same time being a fan of the God in whom he does not believe exists!
If I see a cow in a field with a sign hanging around its neck that reads "HORSE," that doesn't make it a horse!
Such people need to pick one and go with it! They display their intellectual dishonesty from the very start by putting forth a "Pro-Choice Catholic" moniker! It's simply a false "feel-good" tactic that gets them nowhere in the end. And I do mean "the end!"