Can I use Quikrete FastSet Repair Mortar to replace the mortar between stones in a fireplace hearth support?
Quikrete FASTSET Repair Mortar is a great product.  The biggest difference between it and a typical type S mortar is that it is "fastset" (duh) meaning it will be hard in about 20 min.  Not cured, but hardened. And that it is intended for commercial use as it will eventually reach 6000 psi after it's full 28 day cure. This product does not need any bonding agent as it is already added. 
http://www.quikrete.com/ProductLines/FastSetRepairMortar.asp 

Any regular type S mortar will harden in about a day or two depending on the enviorment. And will eventually reach 1800psi
 http://www.quikrete.com/ProductLines/MasonMix.asp

You may think "oooo  stronger is better" but not so with mortar. You always want the mortar to be weaker then the surrounding material (stone, brick, cinder block) That is why it comes in so many strengths. From strongest to weakest type, M S N O K.

Sorry to be so long winded.

Basically, go with the type S, and use the FastSet Repair mortar for repairs around the house.