So I typed out a big long response and deleted it.
I swore off social media a few years ago because of things like this...so I'ma tread lightly here.
Staying away from the gun topic which I have fairly strong feelings about, I'll just give you my grandfather's old saying, since would apply here. "Sometimes there is a right way to do something, but there is always a lot of wrong ways". If that man would have asked you privately, none of us would be talking today.
I'm not sure what kind of expectations we should have for Costco greeters...but I think most here would agree that this could have been handled better. I never would have brought it up to the manager. I'm glad you did. Maybe a little greeter feedback would be helpful.
All the best to your family. I hope things get better for you!!