There is no point to accept, you are wrong to call Celtic a British Club, they are a Scottish Club.....if you accepted that fact then we wouldn't have to keep reminding you that was just the least of the stereotypical claptrap that you psoted in your OP about the Northern Irish.
The Anglo-Scottish Cup was a separate league created by the Scottish and English Football League Associations, it had no Association of it's own, which is why, when the Scottish League pulled out, it was discontinued.
It was not and never was intended as a British League Association and it was never officially recognised or instituted as such by the Association Football governing bodies.
So it is wrong to claim it as an example of an Affiliated British Football Association.
Actually they couldn't especially since 1993 when the rules regarding the Home Nations and player eligibility were codified by each Countries FA.
The FIFA rules are generally thus:
FIFA leave the eligibility of any given player to the countries FA, most countries this is a straight forward thing, as the nationality or more accurately the citizenship of a player and the overall FA are one and the same, however obviously with the Home Nations this is complicated by the fact that each home nations each have a seperate FA and thus they came to an official and legal agreement (not gentleman's handshake) that is as follows:
So basically all FIFA are considering is the eligibility of a Player to register/play for a specific Association, such as the Scottish, English or French FA etc....it leaves the question of who is eligible via nationality to the Football Associations themselves.
So, as the respective Home Nation Associations are all independent and they have a codified system of rules regarding eligibility it is indeed correct to refer to the teams which are affiliated to the respective Associations by their respective Home Nation, for example Celtic are a Scottish Club, rather than a British one.....
Isn't arguing about Football Associations and eligibility far more fun than expressing hatred for the Irish, or British depending on which side of the divide you sit on....