Does a truck need anti sway bars carry a camper?

There were sway bars in the ‘90s and way before then.
The ‘98 F250 is an odd one-year truck with the whole F150 body and F250 running gear... just so everyone else knows.
If I were you I’d set the camper on the truck and drive it. Then bolt a sway bar on if you feel it needs to be tightened up.