The bottom line is that everything CAN change things, brass, primers, bullets, bullet weight, seating depth, case capacity, and on and on and on.
Its best when you change components that you start a bit below max charges and work up.
As to the specifics, yes brass brands and type can change things. I have a Winchester 22-250 that hated nickel brass...but any other brass, rem., WW, or federal changed essentially nothing. I used every brand mixed together and there was no difference, all would shoot way under 1 inch groups.
I got some nickel brass on a good deal for my nephews 7-08 and it likes it just fine. I've used WW and Rem in his rifle, they shoot the same as the nickel brass.
The thing to do, IMO, is once you find a load the rifle likes, just stick with those components if you can. I typically don't switch up anything, I buy everything in bulk...brass, bullets, primers, powder, etc. once I have my chit dialed in. Probably a bit OCD, but I don't like surprises when I'm handloading...and if I change up a major component, I'm at the range with a chronograph making sure all is right with the world.