My rule is ask twice, but the second time being a very simple “are you sure? It’s OK, I’m happy to contribute / half / cover” (delete as appropriate).

In the UK at least there is still a level of “pride”, for want of a better term, with either not accepting charity, or being seen to treat people you care about. There is also an expectation that you should be humble and gracious when receiving a gift so you also should reject it at the first instance. If the offer is only made once then all that is really happening is both sides are playing their parts and nothing else.

The second time is to acknowledge that it was a genuine offer, and not just part of the dance.

If the other person still insists, regardless of what it was, then you accept it. And maybe keep a mental note because next time it would be nice for you to return the favour if they treated you.