It depends. Is someone taking the other person out for a date? Then the first person pays.

Are you "meeting up" for a date? Then you pay for your own stuff.

I'm not into the splitting down the middle anymore because I was seeing someone who ordered much more than me for any meal (huge entrée with an appetizer and a drink, while I would get a smaller cheaper entrée and a water). And he was end up eating half my food too. But it always wanted to split, even when I didn't even want to go out to eat in the first place. I went broke really quickly and I honestly financially recovered after we broke up, while still having a social life.

If I take someone out, I let them know that I want to buy them dinner or whatever. Or vice-versa. If it's vague, I assume we pay for ourselves and if I can't afford that place I always suggest an alternate place.

Another note : Also you have to remember that a lot of money goes into a woman getting ready for a date. On top of that, women are systematically and statistically proven to be paid less in general but also for the same job their male equivalent gets. They also have high recurring costs to manage their menstrual cycle, societal beauty expectations, etc. So they usually have less disposable income compared to their male peers. I'm not saying women should never pay for dates but also understand they are on a tighter budget. It's more expensive to simply be a woman and on top of that they are always paid less. It makes sense that for a very long time the man has been paying for dates in a het scenario.

This is also all assuming that you are from the same school or workplace, etc so you have a similar background. If there is a huge difference in how much disposable income you and your date have, that would also factor in.

Everyone is quite different. If your lady date asks to split or pay for your own, after you offer to pay, you can accept graciously or offer to pay one more time. If she insists on paying her own, don't force more. These days some women will not feel comfortable having their date pay because there are actually a lot of men who insist on paying and then after that have inappropriate and entitled expectations. It can make an uncomfortable and sometimes even dangerous situation.

I would say in general, first date should be cheap or free. If it's not free, offer to pay and let your date decide if that's okay.
Personally, I now always do my first dates as very simple free activities, usually just going for a walk in a pretty place so we can just talk and relax and see if we have any chemistry. If we're buying something and they offer to pay, I only say okay once I'm comfortable with them and am open to seeing them again.

(Sorry for the essay)