Wow, tough question, for what really should be a simple subject.
I see the OP hails from NYC, I think if you are closer to urban areas the stares will go up a bit.
I also agree with Boss1, going to do your laundry in a crowded campsite with a Battle Mistress strapped to your side is creating part of the problem.
I almost always carry a Marbles Ideal, the small one, 4.75" I think. Sometimes folks will ask why. I tell them, I canoe a bunch and always like a knife with me on the water. For my own saftey, as well as others. Then I explain that I would feel horrible if I came across their child drowning and was unable to cut them out of the overturned boat or seaweed. They seem to get that.
More and more, when I know I am going to be among other folks in the outdoors. I try to bring a Saw, an Axe, and a Knife, i work to explain the virtues of all three and associate them all as tools. Not weapons. It always amazes me how people will recoil from a knife, but are perfectly fine with a hatchet or an axe. Perception is reality, you just need to work on changing their perception.
Many folks see no reason for a knife, because they camp just like they live, making use of batteries, generators, precooked meals on paper plates, with plastic knives, forks, and spoons, instant coffee, all done with a bag of charcoal or a jet boil.
I actually just returned from a few days at a state campsite, visiting with some old friends. I was boggled by the amount of radios, generators, and people talking on their cell phones that I saw. That's the stuff I go in the woods to get away from. Some of the campers these folks have are nicer than my house. We just need to educate them that there can be a lot more to it. That with very little extra effort, it can be a lot more rewarding.