Yes you can cook food in a pan or skillet using a rubber spatula just as long as you don't leave the rubber spatula in the skillet or pan too long when it's hot.
If you just use the rubber spatula to flip over the food and then remove it within a few seconds then the rubber spatula should not melt.
I've cooked and still cook using a rubber spatula and never had one melt when I just flipped the food over with the rubber spatula.
However I would not recommend using a rubber spatula to cook on a grill with a flame because the direct flame could melt the rubber spatula.
On a charcoal grill it might be okay but not on a gas grill unless you turn off the flame.