I have an HS Precision on my Remington 700 Varmint. It will flex just a tiny bit but not enough to contact the barrel as it has very wide barrel channel. I have a Savage 110 FLP that came with a factory tupperwear stock. It was flimsy as a pasta noodle when I got it. By using acraglas to glue in a few valve rods in the barrel channel and using acraglas around the magazine box and the pistol grip, it's now a darn club. Of course that added about 12 oz of weight but this is a varmint / tactical type rifle that's already heavy. I suppose you could say that's an inexpensive way to make a cheap stock rigid, but another perspective would be that maybe you really can polish a turd.
I also have two McMillan stocks and they are extremely rigid, plus they are full length bedded (pressure neutral). Those are the only synthetic stocks I have on centerfire rifles, the rest are pieces of timber.