Is vaping in the navy legal?

It's treated the same as cigarettes

You can do it but there are restrictions

If you're caught doing it in violation of regulations and start to whine that "it's just vapor" we will make your life head, a guy in my department tried that back when vaping was new.

Yes, it is legal. However, they are still treated like the typical cigarettes; so, no vaping indoors and/or during missions (the smell and/or the light can give your position away).

It's legal anywhere

Whether or not Navy regulations allow it will depend

vaping is treated just like smoking the old fashioned way.. mostly discouraged/banned in all public spaces/buildings. banned outright on subs and the scuttlebutt is that all surface ships are going to go the same way within the next couple of years.

would not surprise me at all if the sale of all tobacco and tobacco related products will soon end on bases worldwide.

It's the substance that matters, not the method of delivery.

You can use an electronic cigarette, a turkish hookah rig, or a space suit helmet filled with smoke...it's all fine if it's tobacco.

depends on what you vape.
tobacco - yes.
marijuana on the other hand, will show up in your pee test whether you smoke it or vape it.

People vape all the time in the workspace on the ship. You have lots of 18-19 year olds doing it in the workspace where the equipment can get fried but they do it anyway