The potential new employer is free to determine whatever rules they like regarding references. The are no laws which state when they should, or shouldn't, call for references.
When I was in teaching, it was standard practice for schools to invite applications for a post, weed out those that were obviously unsuitable and then seek references for all,/i> of the remaining candidates. The interview list would only be drawn up after reading all of the references.
it would be much better if all employers followed this method. Then they'd know far more about applicants' real potential (or lack of it) before deciding whether it would be worth interviewing them.
You're free to request that the potential new employer doesn't call for references until after the interview stage but, equally, the employer is free to say "If you don't like our way of doing things, we won't take your application any further".
Chris