I was having a chat with a colleague in ministry a little while ago. Does your parish register non-Catholics, I asked. I put the question to our readers, though this isn’t really an armchair liturgist thing.
Spouses of baptized Catholics?
Catechumens before their baptism, and if so, when?
What if someone started coming to Mass, and just said, “I like worshiping here and I like the community. Not sure if I’m ready to be a Catholic or even go to RCIA. I just want to join.”
Would you sign her or him up?
Catholic Sensibility 
Sure. Registration just a fancy word for a mailing list. It has no canonical requirement or effect whatsoever. Your parish of domicile does’t change, nor your parish where your baptism is registered: those are the two key canonical parishes for each Catholic.
About the only thing I can imagine (and this is speculation) it carrying any canonical weight for is that, for baptized Catholics, the pastor of a chosen parish that is not one’s territorial parish could still give you certain ordinary dispensations that pastors typically have faculty to give (like from preceptual requirement to attend Mass or to remit a specific penance, et cet.) I totally defer to canonists on this point.
What is this “signing up” all about anyway? I’ve never felt it necessary to sign-up to any parish I choose to join. Eventually I get onto their planned-giving, so they get my address through that. But otherwise I’ve never seen any need to register my presence in a district with the church (or with the police, for that matter).
It could make a difference if you want to get married and want that church to be the place where it happens. If you’re registered and have been contributing financially and/ or volunteering there, it will get you a lot farther than just popping in to the office and saying you’d like to have a wedding and the stained glass windows would really look nice in the photos. Of course this is assuming that at least one of the couple is a Catholic. Been through this discussion with my adult children.
If memory serves, the pastor of the domicile parish would still have to give permission for the marriage to be celebrated in another parish.
Maybe it varies according to your location. I am assuming that one’s domicile parish is the one in whose geographic boundaries one lives. Around here no one seems to pay attention. My son and daughter in law were married in a parish (in which both were registered members) but in whose geographical boundaries neither of them lived. If any permission had to be granted, nothing was ever said about it. And my husband and I have been members for 20 years of a parish which is not our geographic one.
Oh, I haven’t been a regular attendee of my territorial parish since early February 1991. I do occasionally attend Mass there and go to confession there. I do periodically sample Mass and confession at the parishes within about 5 miles of my home, but otherwise I’m accustomed to a 12+ mile drive into the urban core. Suburban parishes are sort of barbell-curved into a focus on retirees and families with pre-high school children.
In terms of canonical permissions, it seems much depends on how much discretion bishops give pastors. It may be that the domiciliary parishes were contacted by the parish office and that it’s not typically a problem where you live.
Registration trumps domicile in my diocese, although either can grant permission to marry and conduct baptisms.
Liam, as a pastor of a suburban parish, “I resent… er, resemble that comment.”
To answer Todd’s question, no, I wouldn’t register her. One, because I’m not supposed to: somebody in the family has to be Catholic. Two, because it adds to my diocesan assessment and diocesan newspaper bill.
We have a local Excel pseudo-registration list for people such as this so that they don’t fall into the cracks.
In my experience, parish registrations are by family, not by individuals. By necessity you will have non-Catholics on the rolls in mixed religion couples.
Ah, I hadn’t thought about that there was a relationship of the cathedraticum to a parish register.