As long as you work up your load with a given primer it doesn't matter what type primer you use.
Remington ran Lake City Army Ammunition Plant from 1941 till 1985 and used their primers to light off primarily Winchester ball powders. "Normally" magnum primers are used for double base ball powders and below zero weather. Below are photos I found after loading Remington primers and then trying the CCI BR4 primers. Remington primers are called "mini flame throwers" and worked fine in commercial and military ammunition. These primers below were loaded in Lake City 5.56 cases and with 25 grains of H335 and a 55 grain bullet, visually the only difference were the BR4 primers left more soot on the neck of the case. This was shooting these reloads from both an AR15 and a bolt action .223.
Again it doesn't matter which primer you use, all you look for are signs of excess pressure and accuracy when working up a load. I can also tell you with the shortages we had reloaders were using whatever primers they could find. (and no one died and only accuracy "might" have been affected)
Remington Small Rifle Bench Rest Primers #7-1/2
("The priming mix is specially formulated for consistent ignition with a wide variety of powder types, and tested for reliability over a temperature range of -20°F to +150°F")
CCI Small Rifle Bench Rest Primers #BR4
(looks like a wet match compared to above)
The above photos are from "The Rifleman's Journal"
Primer Flash Test Photos
The Rifleman's Journal: Primers - Large Rifle Primer Study
The Rifleman's Journal: Primers - Small Rifle Primer Study
tag_heuer
I'm retired and have been reloading for over 46 years and have never had a catastrophic case failure or even a case head separation. Start low and work up with all your loads, reduce loads when components are changed and work up again. Learn to read your primers and other pressure signs and you will be OK.
Changing from a standard primer to a magnum primer can change chamber pressures approximately 6,000 to 8,000 psi. Now look below at the Quickload chart and internal case capacity of .223/5.56 cases and chamber pressure with the same load of powder. The chamber pressure difference is 6,000 psi and the capacities of H2O were 28.8 to 30.6 grains of water, so primers are only part of the equation.
The above chart was based on using mixed brass for practice ammunition shot from an AR15 rifle at 100 yards or less with the same charge of powder and also mixing primers. (blasting ammo, using up assorted components and be well below max pressure)
And below is what you must learn to read as you work up a load.
The far right primer is telling you the load is too hot and time to back off.
You can also measure the base diameter of the case before and after it is fired.