No it wont. if i was an american, i wouldn't care less who represents the US at the UNSC (the US ambassador to the UN, obviously) but i would definitely care who sits in the situation room and who has an active role in one of my country's most important forums.
... you might not care, and indeed many americans wouldn't, but americans like that are probably approaching half the
reason trump and co is pretty liable to hard screw this country over the next few years. One guy at home shouting at other folks at home, as a part of a committee and held in check by everything involved with that and the position, is a notable problem but not
that bad.
One jackass diddling around
outside of it, acting as representative of country to pretty much everyone and thoroughly pissing off every single other country in the world in the process (and let's not kid, here, unless someone cut out his tongue and removed all his ability to move so he couldn't make rude gestures, that would be exactly what happens), is more than just "bad". It's trade war on the table, looking at a terrorism upspike, actually contemplating the possibility of a land war on home soil, complete clusterfuck. Putting someone like bannon in the US seat of the UN security council would be an experiment in if you really
can completely destroy the political and economic (and possibly military, too) projection power of a superpower in under four years/however long it takes to get him out of the position.
It could be legitimately argued by a constitutional lawyer that illegal immigrants aren't "subject to the jurisdiction thereof" the USA, and if you can get the Supreme Court to rule in favor of that, you can strike down birthright citizenship for children of those who are not citizens.
Well, it could
be argued. Legitimately, no. US jurisdiction covers US soil, period, end statement, do not past go, any exceptions are at our pleasure, there is no second option unless you want to try to force it militarily and ahahahaha. Most of the time if a non-citizen commits a crime on our soil, we will allow whatever country that has normal jurisdiction try them in their courts should said country desire to (largely because most of the time it's not really possible for a single person to do anything worth the trouble of doing otherwise, and it's good relationship building besides). Sometimes we don't, and the latter is
our first prerogative. Even citizens of other countries are under US jurisdiction when they're on our land. The SCOTUS is no more going to rule in favor of that than they're going to suddenly going to start preaching the merits of the sovereign citizen movement (though I guess it may get more likely
some of them do in the near future...).
Other side of that, you're not going to get a judge (and not have it shortly repealed, anyway), much less any legislative body that is not drunk on sixteen different kinds of cocaine spiked rubbing alcohol, to abrogate US jurisdiction on US soil under any circumstances that's not voluntary, towards anyone we do not allow at our largess. That is not a thing that is going to happen. It is not an option on the table, it is not an argument you are going to see entertained other than to be laughed at as soon as the cameras and/or reporters aren't looking, if delayed that long.
... basically, that argument is something that almost sounds reasonable if you have pretty much absolutely
zero experience with our legal and legislative systems. A constitutional lawyer that didn't get their certification from a crackerjack box would laugh at you until you stopped saying what you were saying. Probably keep laughing at you until you went away. Not a line of attack you're going to see employed. About as close to ever as reality can get.
E: Now, removing
citizenship, that's something different. You might see that, and we have legislative grounds to do so under varying circumstances. Jurisdiction, though? No. You're not going to see a precedent that makes that anything even approaching procedural. Allow for exceptions at governmental discretion, yes. No other situation.