As a submariner who wears both the Polaris (an older version that I had to have specially woven in the mid 90s) and the Edzel "Navy" tartan I wanted to chime in.

The most widely available Navy Tartan is the Edzell and many wear it as the Navy tartan in the SAMS posts I hang with. Perfectly acceptable for anyone who is affiliated with the Navy. I have a Japanese friend who was a Physics professor at the Naval Postgraduate School and he wears the Edzell tartan.

The Polaris is my favorite but I have a relative close association with it because I did a patrol on a Polaris Sub (after Holy Loch had been abandoned and the ship had been upgraded to carry Poseidon missiles). I would be careful wearing this if you don't have some association with the Sub Force but I personally would have no problem with anyone from the US Navy wearing it.

When I choose to get a "Navy" tartan kilt I picked the Polaris because the Edzell is more closely associated with the Cryptography community but it has since been more widely accepted as a general Navy tartan.

I have done some research on other US Military tartans and there are now several other registered with the Scottish Tartan Authority including the Seabee tartan and recently a "Beartrap" tartan registered by a US Navy Antisubmarine Aircraft Wing. A beartrap is a type of sonobuoy pattern used for detecting subs.

You can find many military tartans if you type "military" into the keyword block on the STA Tartan Ferret.