There's been a referendum (and may yet be another, not to mention numerous wars of years gone by) on the matter of being joined with the English as part of the United Kingdom - but that's not the same as digging a channel and casting adrift from the island of Great Britain, shared with other British folk such as the Welsh, the Cornish, and even (hack, spit) the English.
I made a comment elsewhere saying that people shouldn't get upset about getting called "British" if they consider themselves Scottish above all. But likewise I don't think it's smart or considerate to be all "well actually..." about something deeply personal and strongly felt like someone's national identity or gender or anything like that. That's sort of asking for conflict.