Wasn't really talking about the U.S., but since you mentioned it... I will point out that the United States has a long and rich history of xenophobic, overtly racist exclusionary immigration policies. If we had not, the country would've gone to pot much sooner.
https://en.wikipedia.org/wiki/History_of_laws_concerning_immigration_and_naturalization_in_the_United_States
Laws excluding any non-white from citizenship, laws precluding Amerindians and blacks from citizenship and voting, laws specifically excluding the Chinese... long moratoriums on any immigration whatsoever...
I'd say all of that and the clearly expressed intent of the founders themselves sort of trumps a silly poem by a self-interested (((poet))) which was added onto that statue's base years after the statue was installed. The poem was not an intended component of the statue.
Of course when you let in outside groups they immediately advocate that you let in more of their group and in some cases they advocate you let in everyone so they don't stick out like a sore thumb, and maybe they're culturally more comfortable with a hodge-podge than the founding stock are.
Anyway, this is off track. The important point here is that it is flat out absurd to act like excluding Muslims from immigrating to the U.S. is counter to the nature of the nation. It is VERY much in line with what America is and always has been. Your mindset is the recent (and soon to fizzle out) aberration here.
Same goes for Europe. Europeans took it for granted until very recently that they shouldn't be permitting a bunch of third world hordes to come in in unlimited quantities because "oh our home countries are awful" yes... they are and always have been awful, because they aren't capable of anything more. It's not a justification for dragging the first world down to that level. It's not a justification for Eurabia.
All nonwhite nations, including where these people come from, carefully guard their own demographics and religious/cultural majority. Only whites are expected to cheer on their own dispossession and vigorously support losing control of the societies their ancestors explicitly built FOR THEM ALONE.