Do not Contact

Is there a way to mark a member's record as "does not want to be contacted" in their profile on LCR?

There is not.

Sometimes wards will come up with creative ways to accomplish this by attaching notes to names or addresses, creating custom callings, or something like that. Please don't do that. (Plus it will save the GSD from having to contact you and remind you not to do that.)

My first step was to change the privacy settings for such families so they would not appear in the ward directory. Unfortunately, a side-effect was that home teachers and visiting teachers could not find them in the directory.

If such families complain about receiving messages from "Send a Message", we move the individual email address to the household email address to prevent such messages being sent to those individuals.