Here's what I've been able to find:
Annotations: Only CHQ can place annotations on the record and it's for members who pose a danger to other members (Handbook 1: 6.13.4)
So, the question becomes how to notate the record. There are a couple of "User Definable Field"s in MLS, but they're only available via custom reports. There's ward geo codes, but that's not practical either. I think the only practical way is to abuse the address or phone number fields.
The directive not to tag membership records with "DNC" (Do not contact) can be found in the
This weekend's tip: No "DNC" on membership records thread. While it doesn't show it now, I'm certain that "birdld-p40" was a church employee at the time it was posted. He still shows a "@ldschurch.org" address. (The "-p40" is for old inactive members when we transitioned the forum between different software.) Of course, that was 8 years ago, I'm sure that message is likely long gone from MLS. I'm sure the sharp-eyed will notice that was published back in 2009 - before the current Handbook.
As for "Members can not dictate the conditions of their membership", Handbook 1: Section 6 has a list of ways that membership can be revoked by the church. Wanting a "DNC" doesn't rise to that level (Handbook 1: 6.7.1), but does show that the member doesn't have complete control. But I would ask if anyone is aware of any organization that would allow a person on their membership roles who demands no contact - not even from leadership. That seems like a terribly one-way relationship.
Certainly there are ways that can be accommodated: The privacy rights in the directory can be set so they will only appear to leaders. I don't think there's anything prohibiting placing them into a special HT/VT districts that are assigned to quorum/auxiliary presidents. Nor is there anything against letting the Ward Council know of the member's wishes.
If someone is really adamant about no contact, I'd consider letting them know how to remove their name from the records. I think most members only know about excommunication - in effect a "dishonorable discharge" and are not aware of the other options available.