One difference between SRP and SPP primers are the hardness of the cup, so some guns (especially ones that have reduced hammer or striker springs) may have trouble setting off the rifle primers. There is a difference in the primer compound itself, the SRP is supposed to be somewhat closer to the magnum pistol primers - more "spark" to ignite powders that may be a little hard to ignite.
FWIW, I am one of the crazy people that like to use the small primer 45acp brass, and I have done a lot of comparison between primers. As a result, I will NOT use regular SPP in my 45acp, I only use small magnum pistol primers, or small rifle primers. None of my guns have a problem setting those off, and I get much closer to the same performance I would get with large pistol primers. (I don't care what anyone says, I've proven that there IS a difference between small and large primers in 45acp).
Based on what I have actually observed I would not hesitate to use small pistol magnum primers, or small rifle primers, in place of regular small pistol primers, if that is all that is available. But, I would work my loads up starting with the min published charges, just as I would do with any new cartridge, or bullet, or powder. I hardly ever load for max velocity anyway.