That's bollocks. I think New Order have always been mostly apolitical but if pushed I think they would reveal they lean towards the left. Certainly Rob Gretton and Tony Wilson were from a leftist background.
gretton and wilson may have been to the left but that doesnt mean the band were to be honest. think the jon savage interview with bernard goes into things like that.
the left is a very broad term anyway, the band may be left leaning on social issues but may well be right leaning economically i.e not keen on socialism or communism.
Playing a gig supporting the miner's strike, perhaps (to name but one example)?
live aid supporting feeding people in africa would be considered left wing but i honestly find it hard to believe that some of those musicians like eric clapton and the coke fuelled junkies who played live aid would be left wing. its not always black and white.
as far as im aware as a foreigner, the actual grievances the miners had were overtaken by the more militant left union leaders battle to break thatcher or vice versa.
miners lost out when it became the scargill v thatcher battle.