Can primaris use firstborn gear?

Lorewise is there anything stoping primaris marines from using firstborn weapons or armor? Primaris gear is cool and all but i wonder if it would not be annoying for chapters like carcharodons who kinda have to use gear that is old, easy to mantain and cheap to produce/repair like MK.V Heresy armor to have to now only use this new Cawl trademarked gear