I used standard pistol primers in my .300 Savage Contander for years in target loads with zero problems. Why? So that I could test the theory that lower primer brissance enhanced accuracy. This was all the rage in the 1980s and many used the special Remington .308 BR cases with their small rifle primers to form wildcats (.22-243 CHeetah, etc.). For me it was far easier to use pistol primers than it was to reform .308 BR brass.
How did the loads shoot? Very well, perhaps slightly better than the loads with standard rifle primers. Note that the .300 Savage was loaded to the 40,000CUP range safe for the Contender, but I used normal .300 Savage powders to do so. These included H322, IMR4320, RL15, W748. The primers looked fine, ES on the chronograph were low, accuracy was sub-moa - some loads agged close to 0.6 moa. I never shot them below 45 degrees F, at lower temperatures they may or may not have ignition problems.
BTW, The Contender does not have excessive firing pin protursion, so I doubt that you will have any issues with light primer strikes.
.