In my experience swapping a primer for an equivalent brand say going from a fed 210m to a cci br2 wont cause a significant safety issue but it definitely may change your load depending on how wide your node is and a bunch of other factors.
Used once fired hornady to load up some 41.5gr H4350 with 140HPBT. Accuracy around a inch, sometimes better. Got some Lapua with the same load and it changed to a consistent half inch for three shots that was repeatable. I didn't think brass made a difference other than powder volume and times it could be reloaded.