The Glasgow club require an 8-4 majority vote in their favour when the SPL's 12 clubs - including Rangers - decide the issue at a general meeting on July 4. Otherwise they face the likelihood of dropping to Division Three.
Both Hearts and Dundee United cited the integrity of the competition as the reason for their decision, with Hearts chairman Vladimir Romanov saying in a statement on the club's website that it was about "keeping order in the SPL".
Romanov added: "Supporters deserve a new beginning and have to accept the fact that their club has to start from the lower keep, keeping order in the SPL and without creating unfair competition with other clubs."
Dundee United said they had come to their conclusion after discussions with fans' groups.
In a statement they said: "The board.. are unequivocal in the belief that a form of sporting punishment must form part of the reasoning behind any decision made and therefore, cannot vote the newco into the SPL."
Inverness and Motherwell have both indicated that they will leave it up to their respective clubs' supporters - but Caley chairman Kenny Cameron gave a strong hint his club's vote would go the same way.
In an open letter on the club's website, Cameron said: "It is fair to say that those who say that Rangers have been punished sufficiently are in an extremely small minority of all the representations received."
Motherwell, who are in the process of moving to a fan-owned model, said they would leave the decision up to the Well Society but regretted the implications would be "substantial and negative under all likely scenarios".
Motherwell's statement added: "The decision-making on 'newco' is rendered extremely difficult by the complexity of the potential scenarios and the uncertainty around the likely financial implications of all of them."
Aberdeen chairman Stewart Milne has denied reports that his club will vote against newco Rangers' application.
In a statement on the club's website, Aberdeen chairman Milne said: "Contrary to reports, AFC has still to reach a final decision regarding the 4th July vote on the Rangers newco.
"This is a critical decision which will have major implications for all clubs and the future of Scottish football. The views of our fans and the issue of sporting integrity will clearly be a major influencing factor in our decision-making."