They're also stiff because they're cheap. Those black or dark brown silver ferrel bridles are usually made in India or China and won't last. The only way to really soften them up is to put coat after coat of PURE Neatsfoot oil on them. Warm the oil up to help it soak in quicker. That will weaken the leather some, but it will prevent some cracking and soften them up a bit. Some of the leather dye may also run as well, so be careful what gloves you use and how you store them.
You normally shouldn't use oil on leather products, but because the leather is Asian and stiff, normal conditioners won't soak in well and really work like they will on quality leather. I normally recommend Passier Lederbalsam for leather softening, but I don't think it will soak in well enough on those reins.