turn it over and read the total watts. If it is less than 1500
watts it should not pop a 20 amp breaker as long as nothing else is plugged into that circuit. If it is popping a 20 amp circuit see if anything else goes off at the same time. If so that is the additional load that is putting you over the top.
The grill should work fine as long as it is along on a 20 amp circuit.
Now if this happened only once at a single campground that campground may have problems or just a weak breaker. Try it on more than one circuit.