The England Cricket Team
Just for a once-in-the blue-moon change, I would like to mention something amusing that refers to general correctness of usage rather than politically correct usage. It does refer to the world's most popular bat-and-ball game so perhaps it might even be worth knowing some day.
When the English cricket authorities send out a team to play matches (called "tests") in Australia, the team they send out is referred to as "the England cricket team". This puzzles some. They think it should be the English cricket team.
It is not really puzzling, however. There are many cricket teams in England and they are all English cricket teams but there is only one England cricket team -- comprised of the best players England can find -- and some of the players in it may in fact be Indians (etc.) rather than Englishmen.
So that is logical enough and one might conclude from it that a team representing Australia would be referred to as the "Australia cricket team". But it isn't. If you referred to the team in that way you would be thought to be either a foreigner or a bit of a nit. The team representing Australia is almost always referred to as "Australia" or "the Australians". "The Australian cricket team" is sometimes heard but it is rare.
Tricky, isn't it? Don't ask me why, though.