At any National Match wether it be Bench Rest, NRA, BPCR you will never find a shooter who is competing having mixed brass. If you ask them they will even admit to weighing their brass... all of which are the same brand name.
They believe that yes, it affects accuracy.
For my 45-70 cartridges - Remington
For my 45-90 cartridges - Starline
And for some, their fine with using any mix for short range target shooting and hunting.