My understanding is that the Stewart tartan, in all its forms, is the Royal tartan and the Queen is its effective clan chief. As subjects of the Queen, anyone can wear any Stewart tartan with the exception of any tartan based on that sett that are reserved to the Royal Family itself (e.g. Balmoral - I think it has a Stewart base to it)

How that applies to anyone outside the UK I do not know but I doubt anyone will be sent to the Tower to be beheaded

Of course, most tartans including the Stewart variations are well out of copyright now anyway so legally there's not much that can be done to stop anyone wearing practically anything they wish to