I did extensive testing of shooting over a hard front rest (a piece of pine firewood) several years ago. Some rifles didn't shoot as well, but some did--but did NOT see the change in point of impact that many people have written about, where rifles shoot higher off a harder rest.
The only time I use a folded towel is when benching rifles weighing less than 7 pounds, where it can really make a difference in accuracy.
Bipods can also affect accuracy if they're rested on a harder surface. The way to find out is to test 'em compared to accuracy from a softer rest.
