Balancing Act

How do you find the balance when you're loyalty is still with your old team but you enjoy the work with your current team and they have somewhat conflicting interests? The only reason why I think there's conflict is probably because of the loyalty and debt of gratitude that I feel for my old team. Or maybe I have a different way of seeing things so that I see some actions as being  contradictory.  Unfortunately, it doesn't help that I don't feel any support from the current team as if I'm on my own and that they don't have my back. Thus, I tend to feel towards wanting to protect the interests of the old than the new.