I have some sympathy with what you are saying but the fact is that is that it was the corrupt business of the old Rangers club that got in the way of the sport. To ignore the consequences of that corruption because it gets in the way of the social side is to condone it. Rangers fans may not like it, but the fact is that the current club is a separate legal entity to the old club even if the social support for the club is the same. If they don't like people pointing that out, they should direct their considerable vitriol at those responsible for the demise of the old club and not at those who defend integrity in sport.
As a public broadcasting authority, the BBC should be making a point of distinguishing the new club from the old. This will be particularly important if and when The Rangers win a major national title. They need to be clear that this will be the first time the club has won this title and not pander to the vitriol of the fans who may like to think it will be the umpteenth time their club has won it. Such a distinction serves as a constant reminder to the footballing world that putting business before sport has a price attached to it