From someone who has ACTUALLY done stuff like this...
Some time ago there was an article in Handloader Magazine comparing, among other things, accuracy in a 308 Winchester loaded with Varget. The best accuracy was obtained with CCI 250 (large rifle magnum) primers.
I've used Federal 215M and/or CCI 250 primers in a variety of cartridges like the 357 Herret, 460 S&W Magnum, 30/06, 270 Winchester and I can tell you it's no problem if you're not already running at the ragged edge of dangerous pressure. That said, for optimal accuracy, you should probably adjust the powder charge and in my experience most of the time you will not improve accuracy by using magnum primers in the smaller cases.