This is different in every state.
In some states, all you really need to do is black-out any official lettering and you're good.
In others, they generally want 51% of it painted some other color.
And some states don't want any of the original color to remain, as it is actually a federally-designated and federally-pushed color that has an actual meaning to it.
Generally-speaking, though, so long as you don't have seats in it, don't have visible (official) lettering on it, and you're not hanging around schools or shopping malls you won't get hassled that much by cops. Worst-case, they stop you and tell you to paint it, and then you can ask them what the regs are. I would bet on most of them not actually knowing it, but some of them might make something up.
If it looks like you're making an attempt, that is usually good enough provided that you're not trying to use it for a daily-driver. Although I've actually seen a couple out locally being used with only blacked-out lettering by a river-tubing company, with something like half a dozen seats left in it to fetch floaters and their tubes out of the river at a certain pickup point.