(This one is for men and women)
The debate on "who pays" still rages on, and for feminists, it's not as simple as "the man" or "the woman." Feminism gets a lot of heat from men who are unhappy with the discourse that demands that men pay for most or all dates they go on, despite the fact that feminists aren't the ones perpetuating it - if anything, feminists are more likely to pay on dates than non-feminists. No I don't have an official statistic for it, but it's pretty fair to assume that someone who believes in gender equality for women also believes that men shouldn't be shouldered with all the financial burdens in a relationship.
First of all, it's important not to assume that just because someone's a feminist, they definitely want to either go Dutch or pay for everything, just like it's important not to assume that all feminists want to be dominant in their romantic and sexual relationships with men in general. Gender equality means that both parties in a relationship pay on dates. Being on a date means that, for the most part, one person pays for both people for each transaction - rather than each person pay for his or her self, which is something friends do when they're hanging out.
Now, if you ask someone on a date, whether you're a man or a woman, you should be prepared to pay for that date. Don't ever take someone somewhere, and then expect them to pay or say "by the way, you owe [X amount of money] for this." If you're expecting someone to pay for something you initiated, you should tell them in advance.
Douchebag story time: this summer a guy took me to the mountains for a weekend, and it wasn't until we got there that he said "oh yeah, you owe $20 in lodge fees for the weekend." Umm, what? I was a bit peeved for two reasons: 1) he hadn't told me that, and probably just assumed that despite being a full time student on a part-time hourly wage $20 would have been nothing; it wasn't a huge expense for me, but it was a substantial amount that I would have liked to have known about before going. 2) I felt that because he had initiated it, he invited me to go with him to a place that was practically his territory (property of a school club he, not I, was a member of), he should have at least offered to pay the fee. Being a feminist, and one who's constantly called out on less-than-feminist behavior, accused of not being a "real" feminist or being a "bad feminist," I didn't ask him to pay lest I risk sounding like a hypocrite. It wasn't a sexist move on his part, but it was a dick move, and one that I'm sure a lot of guys make in their attempts at more egalitarian dating dynamics. But guys, don't do this.
If two people agree to go somewhere in a "what should we do tonight" conversation, who pays for what is a little more up in the air. It can be decided based on who paid last and who has more disposable income at that moment, among other things - it's reasonable to have a dynamic where the person with more money, regardless of gender, pays more than the other. I've been in relationships where I paid more (almost all the time) because I had more money than he did, it just made more sense.
If you feel that you're paying more than the other and you want to make things a little more equal - guys, pay attention - sit the person down and have a conversation about it. Maturely. Without getting mad or making accusations. Before you go out on another date. Do not call the person out while on a date, get grouchy about having to pay, or murmur some hostile, passive-aggressive comment that's only going to bring down the evening for the both of you. This isn't something that should turn into a public argument.
In short, if you want gender equality in the relationship, you need to take gender out of the equation when deciding who pays.