It literally couldn't be any more suspicious. Carrying a jar of bees into a public space isn't illegal either but I'd be very suspicious of anyone doing it, and it doesn't even need any special protection in the constitution.
Just because something is legal doesn't mean you have to be completely and unquestionably accepting of it in public spaces.
Nothing should be suspicious about exercising any of your rights as recognized by the US bill of rights and other constitutional amendments. Any of them. You can choose to be suspicious, but again that's a product of your own misconceptions. A gun is not a jar of bees. I'm not interested in debating straw man arguments. If you have a real argument to make, I'm all ears.
If you are just suspicious of anything "dangerous" without appropriate context then I question your peace of mind.
I was raised around law-abiding gun owners and have never felt unsafe in the presence of a firearm under normal circumstances provided the wielder is not intoxicated or otherwise exhibiting alarming behavior. It sounds like you just aren't used to guns.