Personally, I think humanities majors should be good at math too. (And, for that matter, journalists and politicians.)
Of course the level of math you need to have varies. But I don't think you can be a "good" programmer without understanding logic.
Certainly you don't need the single spearhead knowledge of a single or a few topics that a "math major" gets. And you can probably ignore most of calculus and analytic algebra. But knowing trigonometry and signal theory will most likely make you better and higher paid pretty quickly. Being able to look up and study the math you need at the moment, quite certainly so.
But that doesn't mean that a lot of girls that think they are bad at math should stay away from trying programming. Girls specifically have a tendency to undervalue their own knowledge. (While guys tend to overvalue.) (I personally think this behaviour is social training.)
If you think you are bad at math but programming comes easy, you might find that you weren't actually bad at math.