I agree with this notion; you're doing your duty and you shouldn't be subject to harassment of any kind in the process of that.
However, I wonder if it's fair to take it a few steps further.
I'm no lawyer, but I would imagine if someone were to go to the level of harassing one's social media account(s) and ultimately be beholden to the level of cyberstalking, that should come with a bit more legal bite to it as well. (Note: this is already an option.this is already an option.) I would say that the user doing that sort of thing isn't the kind of person that we want in this community at all, so I would hope for their permanent removal as well.
I've never had to receive a moderator message (that I can recall anyway), and I personally would not wish to lash out against a moderator individually anyhow, but it makes sense to anonymize these messages. No sense in introducing the risk of abuse.