Catholics: would you support the idea of formally dividing Catholics into religious and less-religious or non-religious, but maintain a Catholic identity?

I have always thought that Catholics, similar to Jews, see their religion not only as a belief system; but also, what they are, part of their identity. As you know Jewish people in America, not sure about other countries, divide themselves primarily into Reformed, Conservative and Orthodox groups. Each group has its’ own synogogues and Rabbi’s. I have heard the term “little c” used by Catholics, Daloon used it today, and it made me wonder if Catholics would like to be able to go to church knowing that everyone in that church identifies Catholic, but maybe does not follow all of the rules like no birth control, or maybe disregards confession, etc.

I can see some of the obstacles. Since the church is headed up by the Pope and Vatican, the Pope would probably not acknowledge these priests and churches. I guess that is why many got to the Episcopal church, but it would be hard for me to identify with a different religion even if I did not agree with everything my religion preaches.