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How important is it to keep all metal connections in a climbing system the same?
Should I avoid steel carabiners on aluminum rings or pulleys?
What are the consequences to mixing these metals in a climbing system?
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Actually, steel biners with pulleys is probably a good idea. Many pulley side plates are either thin steel or a bit thicker AL. In either case, as force is applied to the pulley, the thin side plates will cause a concentrated force on the biner.
OTOH, using AL biners with steel pulleys would probably wear a groove in the softer AL biner.
Regarding steel biners on AL rings, The contact area is 'softer' and would not wear as fast as AL on steel pulleys.
But, anytime you put a harder metal against a softer metal, the harder metal will sustain less wear than the softer metal. But, even so there would be possibly the very same wearing effect with AL to AL, except both AL parts would wear essentially equally.
My only caution, as I stated previously, is avoid AL biners with steel pulleys - at least the steel pulleys with thin side plates. Not only is it a hard metal in contact with a softer metal, the force is quite concentrated by the thin side plates. Further, the 'corners' formed by the stamping process can exacerbate the situation.