I think if you join a foreign team for sport you should give up your USA citizenship.
In the same way that I think if you come to the USA from Mexico and become US citizen, you should NOT be rooting for the Mexico national team when it plays the US national team (soccer).
As someone who was born and raised in the US but has spent the last 12 years living in the UK, I can tell you that you seriously underestimate how difficult it is to give up your national identity.
That's especially true when, even if you do change your citizenship, the locals will still refer to you as being from whichever country you emigrated from. Even if you don't look different, you'll probably sound different for the rest of your life. And that alone is enough for people to refer to you as an outsider.
And being cast as an outsider by the people you live with, especially if it's combined with resentment toward outsiders, is enough to push you back to identifying with your native country, even if you have no plans of ever moving back.
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