In Fahrenheit 451, how did Mildred respond when Captain Beatty asked her to turn off the relatives?
Prior to Beatty's arrival, Montag has begun to question his way of life and Mildred stubbornly refuses to give it any amount of thought. During the previous day, Montag witnessed an old woman burning herself with her books. During the burning, Montag steals one of the books. This dramatic sight combined with his talks with Clarisse have led Montag to reconsider why books should be burned.
The next day, Montag stays home from work. He asks Mildred to turn the parlour off and she refuses. When he vomits from the smell of kerosene, he tells Mildred about burning the woman the previous night. Mildred acts as if this is nothing and says, "That's water under the bridge." Mildred doesn't want to hear anything from Montag at this point because he's questioning their way of life. She will not obey someone who might disrupt how she lives.
When Beatty arrives and tells her, "Shut those 'relatives' up" she does so immediately because Beatty is an authority figure. Beatty is one of the people that keeps order. He keeps the work of the firemen going. Mildred is content with her passive life, living vicariously through her "relatives" on her programs, so she needs people like Beatty to sustain that way of life. She obeys Beatty immediately because she fears him but also because she wants Beatty to reestablish order and get Montag back to being a passive, thoughtless person.