I don’t know if Norma is actually talking to you, or if she’s just making a silly joke for Abby’s benefit. In either case, I don’t think you can really become a grammar nerd unless you were born for it.
Whether “woman” is actually a sexist word depends on the origin of “wif.” What did it mean before it meant “female”? If it comes from a word meaning “weave,” then it is potentially reinforcing stereotypes about traditional gender roles. It’s possible, however, that it refers to female private parts. All the resources I’ve found say the etymology is “uncertain.”
It’s pretty pointless that both lights would be red at the same time in the first place… but that’s how it is sometimes, at least where I live. And sometimes, of course, one light is red and the other one is green but still says “Don’t Walk,” because you didn’t press the stupid button in time.