Only if I'm positive he won't have an issue with it - and actions speak much louder than words in this respect.
I would have responded "but of course! What's the big deal?" fiffteen years ago. Then I met, dated, married and ultimately divorced XH.
He was jealous of my job and of my professional success. As in: he quite literally talked about it and behaved as though I were seeing another man. And it got worse as I climbed the corporate ladder.
Ultimately, I think it was a gender thing and that the fact that I rose up the ranks and made twice what he was making three yesrs out of university threatened his sense of masculinity. That he really wanted a woman he could take care of and for whom he could bring home the bacon. And that he resented not having that.
He got married to someone just like this less than a year after our divorce was finalised - and when I accidentally ran into his cousin, she had a massive go at me for having enjoyed years of nice things and then cleaning him out so that he couldn't afford to buy the same stuff for the 2nd Mrs XH and for how this was massively unfair. Cue an angry phone call from XH a few days later after cousin had, apparently, spilled the beans about the fact that I'd been buying my own clothes and cars all along. XH thought I had humiliated him in front of his family by telling her that and was livid.
So, long story short: I would date someone who earns less than me again. I'm a high earner, so I'd be massively restricting my dating pool if I didn't at least consider it.
I most certainly would also, however, be a lot more diligent about whether or not a bloke's ego can genuinely cope with me being the main earner in the couple. I most certainly wouldn't ever want to repeat the experience with XH ever again.