Bloodsworn could mean the Kor'Kron that are under Garrosh's command, orcs like this kinda thing. I don't think it has anything to do with the Mogu.
The Mogu likely think themselves above Garrosh. That said post killing Lei Shen, could be a thing.
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I've never really seen much of this bloodsworn, but given they are a band created by Garrosh, you would think in the coming events we would either see them and fight them, or when garrosh is gone, we see something of them being assigned to the new warchief, or them disbanding.