I don't see what's wrong with having both ninjas, guns and cars in the same universe.
Not everyone is going to go spend their highschool years in a ninja oriented highschool, as opposed to one focusing on art or music or business or computers. I figure ninjas, as they're portrayed in naruto, are more or less people with a bachelor's degree in ninja magic. I'm not entirely certain how one would legitimately earn a living doing ninja'ing though. Plus, using ninja magics/skills to build houses or heal people might start to wander off the ninja theme. (doctor mcninja)
Plus, didn't the original naruto prototype manga have a gun in it? Some guy shoots naruto's friend and then naruto decides to hunt down the culprit?