There is no need to worry about the people legally carrying guns, and the people you need to worry about will not necessarily be carrying guns. If you see someone openly carrying a gun, it's not considered polite to point and stare. If you just forget about the guns, you will find the U.S. to be very much just like Canada, only with different accents, and with an automatic assumption that you want a cup of coffee with breakfast.
When the OP said "below the border," my first thought they would be nuts to go camping in Mexico! Back in the 70s when I had a company running birding tours to Mexico, we always put in our pre-tour information that if you had to have tea with breakfast, bring your own. There was nothing quite as fearsome as a Canadian at breakfast who had just found out the hard way that tea was not a common offering in restaurants in Mexico.
A few months back, we were camping at a model airplane meet, and it was all over the local news that two armed fugitives were at large in the area. One of our Canadian friends (female) was going around saying, "If they come here, they'll see our license plates and know we don't have a gun! I want a gun!" We considered offering her one but decided discretion was the better part of valor. They finally found one of the feared fugitives hiding up in a tree and used a fire hose to get him down.
Please, forget about guns and just come on down.