They have been paying lip service to honour the referendum result because (approx) 60% of Labour constituencies voted to Leave but they have been backtracking on their promises and manifesto commitments for some time. As for any future referendum ... the vast majority of Labour members back Remain, the vast majority of Labour MP's back Remain, most people in the Shadow cabinet back Remain so I would say it's virtually certain they would support Remain (possibly even while claiming they weren't)
By any reasonable analysis, Labour's Brexit policy is an absolute farce. Negotiate a 'fantastic' new 3rd deal ... then campaign against it offering the country a choice of Labours Super Soft Brexit or Remain. Obviously undemocratic loons would think that's fine but I'm guessing the vast majority of Leave voters and plenty of democratic Remainers would be outraged .... rightly so.
and of course there are plenty of democratic Remainers who will vote in support of remaining because there is no mandate for any particular 'leave' option (e.g. even arch leaver Farrage says the Johnston deal is worse than remaining) and there is a high possibility that the majority will wish to remain now.