Those who oppose the right of motoring organisation to check books provided (6)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

AA (abbreviation for the Automobile Association), containing (check, as a verb = control) NT (abbreviation for New Testament = books) + IF (provided = on the condition that). Short for “anti-fascist”: a name for various activist groups set up in opposition to right-wing militant nationalism.