Be careful not to over-suppress.
What do you do when someone calls and asks to be taken off your mailing list? Do you just say OK and pull them from all future communication?
The better solution is to engage them, and use this opportunity to build a deeper relationship. Try to solve their desire for reduced communication but still keeps them connected and seeing your messages. It is best if you’ve got some options available to you (i.e., bi-monthly, quarterly, Christmas only, newsletter only, etc.). Train your staff not to over-use these mail flags.
I know of one organization that was aggressively categorizing donors as “newsletter only” if they complained at all about getting too much mail (even if they didn’t ask to be sent newsletters only). This over zealous flagging resulted in them losing $3 million over five years.