It does, when he’s in Canada.
When he’s in America, we apply American law.
To carry this to an absurdity, let us assume Chad passes a law that the children born to American diplomats while they are serving in Chad are Chadian citizens and are NOT American citizens.
Our response would be, as it should be, “That’s all fine and dandy, Chad. You pass whatever laws you like and apply them as you see fit. But we don’t base our decisions about American citizenship on the laws of a foreign country.”
The USA has always just ignored the issue of dual (or more) citizenship. If I become legally a citizen of Chad while retaining my American citizenship, I may acquire new obligations to Chad, but my rights and duties as an American citizen change not at all.
Unless of course I renounce my American citizenship, but again that is determined by OUR laws, not those of a foreign power.
Extra credit to anybody who gets the obscure SF reference to Chadian citizenship.
I don’t know whether you’ve been in on the discussion, but 3 of our first 4 Presidents were declared citizens of France by the French Parliament.
Yes, it was out of honor. But it seems to have carried with it all privileges of French citizenship.
So George Washington, Thomas Jefferson, and James Madison were all French citizens - WHILE serving as President.