i think that is should all match especially if you are showing
For at home riding or just lessons I think it is fine (personally I like having my tack matching always), but for showing it is a must that the leather products you have are either all black or all brown.
Use the brown at home but black at shows. You look more put together
It's not that big of a deal. People mix and match tack colours all the time! I have a black bridle and a brown saddle. If you're really worried about it then you can buy a black bridle for showing. It honestly doesn't matter it's just your personal opinion whether or not you want it to match.
Buy a black bridle for shows, use the brown one at home ;-)
Sun bleaching your saddle is usually a bad idea as it can damage the leather. I'd trying staining the bridle or getting a new one.
Leave your saddle out to sin bleach it