@revelette1,
Lower courts have vacated the travel ban on the basis of the 14th amendment's initial paragraph which guarantees equal protection of the law. This is that paragraph in its entirety:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Note that after addressing the rights and privileges of citizens, it refers to "any person" (which I have highlighted). This has been interpreted in the past by the Supremes to refer to absolutely anyone. In
Yick Wo versus Hopkins (1886), the court held that any law which is race neutral on its face, but which is prejudicial in its effect violates the 14th amendment. In the majority opinion, the Court held that:
These provisions are universal in their application to all persons within the territorial jurisdiction, without regard to any differences of race, of color, or of nationality, and the equal protection of the laws is a pledge of the protection of equal laws. Note the highlighted part of the text. Courts which have vacated the travel ban are not required to address the issue of religions, because it blatantly discriminates on the basis of nationality.
Yick Wo has been cited well over 100 times by the Court, and it would be a serious violation of precedent to ignore that ruling, which has been a part of so many later decisions, in particular beginning in 1950 with the Warren Court, as it struck down so-called "separate but equal" provisions in public accommodation.
I seriously doubt that the Roberts Court wants to revisit so many seminal rulings in the last more than 60 years.