I understand this from the perspective of having tolerance for women who do allow men to pay (i.e., it doesn't make one anti-feminist), but generally speaking I don't buy into the "man pays" orthodoxy. As mentioned below, it is from a bygone era and giving it some form of life support, even if on modernized terms, is just prolonging its inevitable demise, imho. Ultimately it shouldn't matter who pays. Simple as that.
My partner and I have been together for 23 years. We met at university, studying fine arts—choreography for her, music composition for me—so neither of us had money, and we almost always split the bill. Or it would be a "get the next one" situation, as mentioned in another comment. To me this is respectful and real and doesn't allow any strange ulterior motive to interfere with the occasion. All the psych 101 bullshit about what you may or may not be 'signalling' doesn't really mean anything, when it comes right down to it. You'll have to get past all that if you hope to have a meaningful relationship anyway, so why not start from day one? If I went on a date with a woman who's nose fell out of joint just because I mentioned splitting the bill, I'd most likely not be looking for a second date. Not because I'm cheap or 'unkind', but because it would be a red flag to me that there's a bunch of other Olde Worlde expectations waiting to submerge the relationship down the line.