That’s the precedent I see: target a given country.
Problem is Trump specified (and many here support) restrictions based on _religion_ on grounds that conquest is a core principle of the religion in question, that even “moderate” adherents internalize proselytizing-thru-conquest as axiomatic, so there’s a legit question about whether that poses a threat to this country via immigrants. I’ve not resolved this one personally yet, holding “freedom of religion” and “rule of Constitution” as core principles.
I think stopping immigration on a per country basis is more practical. On the other hand, Saudi Arabia is (excluding foreign workers) 100% Muslim and Pakistan is 95-98% Muslim, so whether you want to call it excluding Muslims or excluding Pakistanis and Saudis, I am not sure there is much actual difference. It gets trickier with more mixed countries, but that would be a start. But to your point on the Constitution, as far as I am aware the US Constitution does not protect non-citizens who are residents of other countries. It really has nothing to do with them and the US has an absolute right to exclude any non-citizen (and possibly non-permanent resident, IDK) that it wants for any reason or no reason at all without violating the Constitution. I have not seen any serious argument to the contrary despite all of the handwringing. That is, no foreigner has the right to immigrate to the United States and we could, without offending the Constitution, exclude all redheads or all fat people or whomever we wanted, without any constitutional limitation.
False arguments begin advanced by people in the "News Media" and politics who have a very superficial understanding of the law.
https://www.law.cornell.edu/uscode/text/8/1182
(f) Suspension of entry or imposition of restrictions by President
Whenever the President finds that the entry of any aliens or of any
class of aliens into the United States would be detrimental to the
interests of the United States, he may by proclamation, and for such
period as he shall deem necessary, suspend the entry of all aliens or
any class of aliens as immigrants or nonimmigrants, or impose on the
entry of aliens any restrictions he may deem to be appropriate. Whenever
the Attorney General finds that a commercial airline has failed to
comply with regulations of the Attorney General relating to requirements
of airlines for the detection of fraudulent documents used by
passengers traveling to the United States (including the training of
personnel in such detection), the Attorney General may suspend the entry
of some or all aliens transported to the United States by such airline.