B737-700 Captain reported heavy rain on approach to landing and elected to make a go-around due to visibility issues. Reportedly; the hydrophobic coating on windscreens is ineffective.

Narrative

Heavy rain at ZZZ; first leg with this aircraft so no knowledge how well the hydrophobic windshield coating or wipers worked. RNAV XXL to minimums. Poor rain shedding; even with wipers on high. Unable to see the runway environment at DA. Go-around and accomplished. CATII Runway XXR. Still heavy rain and runway environment now acquired until just above minimums. Runway difficult to see even between wiper swipes. Landed safely. FAA inspector on Jumpseat was not impressed with the visibility of the Boeing. Also; when ATC questioned the go-around; Controller asked if we were not on the Approach. Apparently other aircraft we're getting in using this procedure. They were not aware Company was not approved. Approach handed each aircraft over to Tower at the FAF; which was an extremely busy time to run checklist; remain established and hear what the previous aircraft was experiencing. Had it been necessary to go around this again I would have declared minimum fuel and possibly emergency fuel to get to a suitable airport without rain. Dispatch offered negligible help while we were in hold and no current radar reports of rain intensity.