Batter hits ball to left field fence, base ump signals obstruction on 1st, runner trying to score is called out on a bang bang play at home. easily would have been safe if not for obstruction which again was called. they let the out stand, was this correct?
This is a "had to be there" to tell. Based on the information you gave, sounds like a good call.
By rule the runner is only protected between the bases where the obstruction was called. At the time of the call the umpire is supposed to decide what base to award at the time of obstruction and can award more than the base the runner is heading to. It is very rare that anything beyond the base they are heading to is awarded.
Hope this helps