A: Your 4-year-old is still too young to be polite simply because you've explained it to her. She won't start caring about social rules and etiquette until she's 7 at the earliest. Until then, set basic expectations for politeness -- perhaps she needs to look a person in the eye and say "hello". See what she can agree to do, ahead of time. Then enforce your rule: Reinforce her by allowing her more family activities and fun when she's polite and remembering her manners, and be less generous with rewards and outings when she forgets the basic rules. But don't scold and fuss over her -- just be matter-of-fact about your expectations, make sure she agrees with them in advance and is capable of following them, and give the consequences you've laid out for her. Scolding will only start a power struggle that you can't win, long-term.
I'm also wondering if she's shy. Shy children have a much harder time following social rules because they're naturally more introverted, and need more support, encouragement, and practice. They may move slower, socially, but it's not their fault. Shy kiddos can learn to be polite too, it just takes them longer, and requires more patience and encouragement.