I'm pretty sure the only race/job combo that actually had racial stats that mattered was Dunesfolk for lv50 BLM; with SCH they could get an extra fire cast out under Astral Fire, I believe (I'm not a BLM, so this is secondhand info for me. Had a friend who was considering changing to boost his DPS and talked to me about it)

At 60 though...no, the racial stats don't matter at all in combat. There may be a node or two that is race-blocked, but IDK if there are.