I know I was always taught too that hydrogen peroxide can bleach out colors but so far I've definitely had no problems and I use it all the time. My carpets are a beige and I use a lot of hp when I clean them too. I've also used it on my couch and my bright red curtains with no problems! If your hesitant I would definitely do a spot test before treating a large area.
I did on my curtains b/c I was a little nervous about them.