Urgh, are you sure you want that kind of stuff? Michael W. Smith is just not good music, and the newsboys?
The kind of non-sacred or non-classical Catholic music you are looking for is kind of rare because (practicing) Catholics in general think about music in a different way than Protestants.
I was raised non-denominational fundamentalist and when I was a kid I listened to Petra, Carman (how this guy is popular beats me, I even went to a concert), Michael W. Smith, Newsboys (“I don’t want your sex!”). Now, as a Catholic adult, I see that as inferior music because it really is. It’s like non-alcoholic beer, even the best is not as good as the real thing. I mean, Petra’s sound is not as good as Van Halen (the band they are trying to imitate) with lyrics that are lacking, from a poetical standpoint. Most of these so-called Christian Contemporary bands simply try to sound like a secular band, with “Jesus” substituted for “baby”.
Catholics, unlike fundamentalists, are allowed to listen to “secular music”. You just have to listen to music that is not offensive to your beliefs. Not all music that is secular has lyrics about killing, hate, sex and drugs. It’s also not necessary for music to be written by Christians in order to be able to listen to it. So, there is not really a “Catholic Contemporary” subgenere in existance.
Perhaps you’d be better off asking for secular bands that are not anti-Catholic or anti-Christian? Because if you want proper Catholic music, then it’s going to be liturgical chant- that is “Catholic music”.
Ps. Aside from Perotin and Leotin, those composers made plenty of secular works.