What effect do Montag's rantings about their thoughtless world have on Mildred?
In general, Montag's rants at Mildred have very little effect. This is because she is symbolic of the censorship and ignorance which is so deep-rooted in their society. We see this in Part One, for example, when Montag rants at Mildred after burning the woman in her house. He tries to open up to Mildred and she responds by saying that he is late for work. Next, when he asks her if she has ever been "bothered" about something important, she cuts him off and changes the subject by commenting on the arrival of Captain Beatty.
Similarly, when Montag reveals his hidden collection of books to Mildred and pleads with her to read them, she is defensive but then displays extreme passivity. We see this through Bradbury's description of her body language:
She sagged away from him and slid down the wall, and sat on the floor looking at the books.
In other words, Mildred has no interest in looking at the world from Montag's point of view. She maintains this disinterest in books and knowledge throughout the novel, despite her obvious unhappiness which is demonstrated by her suicide attempt.
If you are talking about the rant that I am thinking of, it does not have much of an effect on Millie. The one I am thinking of is the one at the beginning of Part II.
In that case, he is talking about how bad their world is and how little they think. He is talking about how he watched her get the snake put in to pump out her stomach. But she does not really react.
She does a couple of things. First, she starts talking about the White Clown and the parlour walls and stuff. Second, she thinks that he is just being silly. One way or the other, it really doesn't make much of an impact on her.