Baptist regularly drinking rum in conflict (2,4)
I believe the answer is:
at odds
'in conflict' is the definition.
(I've seen this before)
'baptist regularly drinking rum' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'drinking' means one lot of letters goes inside another.
'rum' becomes 'odd' (I've seen this before).
The alternate letters of 'baptist' are 'ats'.
'ats' placed around 'odd' is 'AT ODDS'.
(Other definitions for at odds that I've seen before include "At variance (with)" , "On bad terms" , "In disagreement or dispute" , "In disagreement or conflict - like bookies?" , "In conflict with, oppposed to (2,4)" .)