Is it illeagle to have blue strobe lights on a civilian vehicle in New Mexico. They won't be used on streets.?

Check with the Arizona DMV or Secretary of State to be absolutely certain but most states reserve Blue Lights for Police vehicles - Some states assign them to the use of Emergency Fire or Medical Responders, In Colorado Blue is assigned to Snowplows.

I believe all states permit Yellow rotating or Flashing lights to designate Service Vehicles and Private/Commercial Snow Plows operating in and near the right of way. Some states permit Yellow and Red combined on Tow Trucks.

Red White and Blue are generally reserved for official emergency vehicles.

It is not illegal to display blue lights on a vehicle in the state of New Mexico. But, strobe lights are different, you should check into it, call the MVD or check their website.

I know that it is illegal to display blue or green lights on a vehicle all over the UK.

Common sense would say that it would be the same in most countries

Yes, having a blue or red light (doesn't even have to be a strobe light, even the neon kits under your car that are blue or red is still illegal. Green or Yellow is the only color you can use.

YES!!

It emulates the idea that the vehicle is an emergency vehicle.

And that my friend, is called IMPERSONATING A POLICE OFFICER/VEHICLE.

Research it.