While there's no doubt that neon underbody lighting looks cool, the laws regarding its use is restrictive in some areas. Exterior lighting restrictions and enforcement is generally up to local and state jurisdictions, which means that neon underbody laws can vary not only from state to state, but from county to county. Every jurisdiction is different, but most have the same basic laws; call your local highway patrol office for specifics.
In general, any color specifically assigned to emergency vehicles and law enforcement is frowned upon. These always include red and blue, but can also include amber or white. The only colors almost universally approved are purple and green.
No car can show red at the front or white at the rear while in drive. These are known as "illegal light patterns," which are mandated against for safety reasons. Inattentive drivers are often caught off guard by such illegal light patterns.
Aside from the fact that visible tubes are a major fashion faux pas, they're illegal in many places. Although they're fairly harmless in most cases (after all, store-fronts use exposed neon tubes), they can theoretically blind a closely following driver if installed on a jacked-up pickup truck.
Flashing or strobing lights fall under the auspices of "mimicking an emergency vehicle," so they're illegal almost everywhere. This includes color changing LED or "plasma" lights, which usually cycle between purple/white/blue anyway. Neon systems networked into a car's sound system may or may not be illegal, depending on your jurisdiction. Most sound-controlled lighting systems "pulse" more than they do "flash," so it's a bit of a gray area.
Like almost any kind of modification used on any car, no lighting system is likely to be illegal if you don't turn it on. This is one area in which LED systems "shine"; most offer the driver a number of lighting options, so you can turn the offensive colors off while driving and back on once parked.
