My fear is that the hair will become brittle and break.
Well, hair of any kind (be it human or equine) is nothing but dead cells anyway, even when it's hanging from your head. So treat the horse hair on the sporran just like you would any other hair. It can be shampooed, conditioned, brushed, etc. And indeed it does need to be conditioned from time to time or it will dry and turn brittle and break, just like the hair on your head would if untended.