I was actually thinking of the same exact analogy- of having a monastic order and lay people with varying levels of commitment, but didn't put it in my reply because I couldn't think of a clear way to not overuse the analogy.
Nobody would say the Catholics are a group of lay religious people that also happen for some reason to overlap in membership with another unrelated group that enjoys monastic lifestyles. The monastic lifestyle is a central key part of the religion, even if it isn't what every Catholic chooses to do. It doesn't describe the entirety of the religion either. Both the core group that follow the full lifestyle together in person, and more distant or less involved participants are all together the same movement- with both the Catholics and Rationalists.
Importantly- when one criticizes the actions of Catholic monastics, it is considered relevant as criticism of the entire organization and religion, unlike the bowling example you gave. People do rightfully blame the Catholics for things like the Spanish Inquisition, and for protecting child abusers and rapists in their monastic communities, even if the average lay person had no involvement in these beyond supporting the religion financially and socially.
One could be a Mormon and fundamentally disapprove of bowling, even if a lot of other Mormons do it, but you probably aren't going to make it as a Catholic if you think monastic lifestyles are immoral or harmful. You probably won't make it as a rationalist either if you think things like utilitarian ethics, and nonmonogamy are immoral or harmful.