This is interesting because you equate being Scots with being a particular group of people: those who come from a particular faith. Any Scots who are not from that tradition are hyphenated-Scots: Irish-Scots, or Catholic Scots or Irish Catholic Scots. That's how you are able to justify to yourself the word "unique" in relation to them and it's how you can also use the term "cousins" when commenting on two or more football clubs formed a century and a half ago by people who were not Scots Presbyterian.
This apparently innocent terminology is at the heart of exclusion and bigotry up there.
Your interpretation of the term says more about your mindset than mine tbh!!
Your outdated view of religion and it's influence in Scotland and it's ability to include or exclude certain factions of it's population are to say the least naive, the polarisation within Scotland today is undoubtedly political and whether you're a part of Sturgeon and her party's determination to Seperate Scotland from the UK or not!
Don't be confused and fooled by the football related "nonsense" by either side as a barometer of how things are up here!!
In the main the vast majority of Rangers/Celtic supporters live in relative harmony equally together.
The Catholic/protestant thing outside of the football affiliation is
pretty erroneous, as I'm pretty sure a very high percentage of both sides support don't actually attend church/Chapel and are more secular tbh, so don't "practice what they preach" so to speak!