Scotland can never be a healthy, modern, independent nation as long as it continues to hold fast to its so-called "Celtic" identity. This is because a modern state is made up of all its contemporary constituencies. If it is not then it becomes an Israel or apartheid era South Africa. Goodness knows what "Celtic" actually means but it is obviously based on biology. This means that any citizen of an independent Scotland who is not biologically "Celtic" will never be a true Scot.
The Irish do not have this problem to any great extent because they mostly regard themselves as Irish. They got rid of their sectarian temptations when they ditched the Roman Catholic Church recently and are rapidly becoming a healthy, cosmopolitan, modern state, albeit a completely broke one.
The English, more than any other nationality in the British Isles, have learned that harking on about original peoples is always a bad idea. The last time a nation got all proud about being Saxon they ended up starting the Second World War and committing the worst acts of genocide the world has ever known. That war very nearly destroyed us and we have been very wary of patriotism ever since.