I know Christians shouldn't listen to secular rap or hip hop music, in which I stopped recently,
but what if the song doesn't contain anything about killing, drugs, and sex? Is it okay to listen to it?
There is no prohibition on any particular musical style. The problem is that certain styles of music are frequently used to promote sinful practices. As you noted rap music often deals with themes of killing, drugs, and sex. Though I don't usually listen to rap, I do get subjected to it by cars driving by with the volume cranked up. More often than not the lyrics are filled with cuss words.
Jesus noted that you are as you think. "For from within, out of the heart of men, proceed evil thoughts, adulteries, fornications, murders, thefts, covetousness, wickedness, deceit, lewdness, an evil eye, blasphemy, pride, foolishness. All these evil things come from within and defile a man" (Mark 7:20-23). When a person fills his mind up with thoughts of evil or even evil expressions, it is highly likely to influence his thoughts at other times, his language, and his actions.
Sin is hard enough to battle without giving it access to our hearts. It does matter if the song is written in hip-hop or country-western style if it is promoting sinful ideas, it doesn't belong in a Christian's life.