Resolutely oppose woman out with gay man (5)
I believe the answer is:
beard
I believe this clue is a double definition.
'resolutely oppose' is the first definition.
(beard can mean to face or confront)
'woman out with gay man' is the second definition.
(woman accompanying a closeted gay man)
(Other definitions for beard that I've seen before include "Vandyke, perhaps" , "hair extension" , "where food sometimes trapped?" , "SECOND PART OF 14" , "Hair on the chin" .)