I think people are mingling 2 things that need to be considered apart.
My personal preference is:
Individuals: that the term “Catholic” be used for those whose thinking is currently more or less with the Pope as Vicar of Christ. I think G K Chesterton was Catholic before he ever joined a Catholic Church. If someone identifies as Catholic, I am not in a position to judge they are not, even if they don’t go to any Catholic Church or belong to another, or are a horrible sinner but not yet excommunicated.
groups: We can’t judge individuals, but we can judge groups. I believe a parish, congregation, denomination or institution isn’t Catholic unless it is in direct relationship to a Catholic diocese, ordinariate, or in some other way directly under the Magisterium. By my view, most American colleges founded as Catholic are not so, at present. I also would not consider a parish in the Continuum or LCMS or PNCC as Catholic, though it may be filled with individuals who are, and very good ones, and in some cases sacraments or orders considered valid by the RC.
Then again, that’s just my preferences, based on how crucial I view the Magisterium as part of the definition of Catholicism. Perhaps some new category of “Via Media” be developed that would include those who would want to be thus classified. I can’t even persuade my wife to agree with any of my preferences, so my chances with strangers on the internet…
