It's not really possible to avoid alienating regulars 100%, so the best you can do is treat them fairly.
When I had newly returned to clubbing a few years ago, my CF at the time mentioned that some dancers were really territorial of their regular customers and asked what I thought about that. I told her that if it was like that, they should be dating. I think she was trying to figure out how to respond to a dancer she saw as competition. In other words, you could mention a buddy who had a really territorial regular dancer who got angry when he would tip or get dances with other dancers.... and ask her what she thinks about that kind of situation. The dancer who told me that story said that I should feel free to get dances with whoever I want.
If a dancer would forbid you from getting dances with others, you might want to ask yourself how much you really want to interact with her.