For over 30 years I have been listening to both sides of the argument about which primer to use in the .357 magnum.
Now most of the manuals and powder guides show magnum primers in their load charts. But as many other long time reloaders, I learned a long time ago that for 85% of the .357 magnum loads out there standard small pistol primers will work just fine.
I had the opportunity to ask an executive of a major powder/ammunition company about this about 20 years ago. What he said was that the average difference in muzzle velocity was about 15-20fps but that the magnum primers created a different pressure curve. There was a larger spike at the beginning of the burn.
So that by developing all of their load data around the use of magnum primers, if anyone were to substitute standard primers the slightly lower pressures would still be completely safe.
But if they had developed the data around the standard primers and the reloader substituted magnum primers, then pressures would be raised. Possibly into the danger zone.
And since a lot of people automatically assume that since the cartridge has the word Magnum in it's name then it must need a Magnum primer they decided to err on the side of caution.
If it were me, I would buy a single pack (100) of small pistol magnum primers of the same brand.
I would load 50 rounds of 4.5 gr of Titegroup in .357 mag brass. 25 with standard primers and 25 with magnum primers.
I'd also load 50 with 4.7gr (25 of each primer) and then another 50 with the 5.0gr load (once again 25 of each primer).
I use different coloured "Sharpie" markers abd draw a ring around my primers to signify different loads. I bought a package with about 10 different colours at Sam's club.
I'd shoot them all the same day and see which gave me the best accuracy.
If the standard primers yielded at least acceptable accuracy, or if they were the most accurate, I'd go ahead and use them.
However if there is a big difference in accuracy with the magnum primers, then I would switch.
After all, reloading is about what performs best for you.