What we have here is an equivocation

Specifically, "Catholic" can (it really can!) mean two, quite opposite things. Of course, what Catholic is supposed to mean is also supposed to get skeptics really annoyed when we point it out.

Catholic can and is supposed to mean "Universal": the Catholic faith is good for everybody, and God whom we worship is God of all, though that's not what he has usually called himself.

But, on the other hand, Catholic can mean "Christian" — you know, those funny folk who talk about turning the other cheek and heaping coals behind your back and have that Nicene Creed thing... or even more weirdly, those Papist Romanizing so-called "Christians", with their surfeit of holidays and authoritarian reading of scripture and... you know, a tiny sect, and anything but universal.

In the latter sense, and in so far as the latter sense remains that understood by everyone who says it, no, God is not "catholic". God does not belong to sects, in either sense of "belong to". That "sect" belongs to Him, but that's another matter.

God is good for everyone; lots of people don't know Him yet, and a few actually hate Him. One Church knows of Him what He Himself has revealed.