"Are AUX restricted from serving as Coxswains in surf zones or from serving as boat crew members on USCG Motor Lifeboats engaged in surf ops within a surf zone?"

The exact wording in the AUX Ops Manual (Chap 4 E.20 Surf Zones) "Auxiliarists shall not operate surface facilities in surf zones."
 
An Auxiliarist augmenting at an active duty Surf Station and who has properly qualified on the Station's vessels may act as a Crew Member per the applicable COMDTINST's, OP Orders, and Station's instructions for that given vessel.