I do not think the issue is "are campgrounds safe". Why is that any different than the local grocery store? or gas station? or where ever else you go. They are all made up of people we have not met before usually and we have no idea of anyones intentions at any time. I have never felt unsafe at any of these places yet I choose to be "prepared". I always have it on me to prevent theft, as long as I have it no one else can get it....at least without a fight.
To arm yourself or not is a personal decision and takes a commitment to training and researching the laws of the states you will travel to. There are states I will not go to because of their stance on my right to self defense..... if only they were so staunch about safegaurding that as they are about what bathroom I should use I might spend some time and money with them. Again, personal decision.
Having a firearm is not force field against bad things happening to you and the
fact is we never know when disaster (or evil) will strike..either be prepared and have a chance to protect yourself or be willing to be a victim. Personal choice.