Let me see if I can rephrase usefully. (I suspect you just aren't using the word "dealbreaker" conventionally.)

Imagine that people who look at your profile are scoring you, with some traits worth points of various amounts (positive or negative). If you've mentioned enough things that earn you points and left out enough things that cost you points, you may get scored high enough that you get a message. Leaving your income off might lose you points, but you could probably make it up in other areas. For instance, I'd estimate that the "point" cost I assign guys on OKC for leaving income blank can be approximately compensated for if they announce that they want to have children someday. The guy who leaves out income but wants kids does about as well with me as the guy who says he makes some modest amount of money and doesn't mention children anywhere.

A dealbreaker is a different thing. It's negative infinity points. It doesn't matter what else you put on there if you also advertise a dealbreaker (there is no corresponding "plus infinity points" here) - it doesn't offset or compensate for positive traits, it renders them irrelevant. For instance, I wouldn't ever date a guy who smoked cigarettes. This doesn't change even if he looks like Sean Maher and has every nice thing to say in the world about marriage and children and we have identical tastes in music and he lives a block away and he's a vegetarian and we're a 99% match according to our questions and every paragraph in his profile is a masterpiece of humor and insight - smoking gets him a big ewwww, and while I'll wince as I close the tab, I will not message him unless it's to tell him that I wish he'd quit.

If more women message you when you start advertising your income, some of them might be doing so because you removed a dealbreaker. I would expect far more of them to be doing so because you've crossed a point threshold.