Citizens likely have an absolute right to enter the US. This hasn't been addressed directly by the Supreme Court, but here are some cases that come close.
The Fifth Circuit, in William Worthy, Jr. v. US, 328 F.2d 386 (5th Cir. 1964):
We think it is inherent in the concept of citizenship that the citizen, when absent from the country to which he owes allegiance, has a right to return, again to set foot on its soil.
The Supreme Court, in Tuan Anh Nguyen v. INS 533 U.S. 53 (2001) said that conferring citizenship on a person would give "the absolute right to enter [the US]". This wasn't necessary for the holding in this case, which was about whether the person was a citizen, so this could be considered dicta.
Fikre v. FBI, 23 F. Supp. 3d 1268 (D. Or. 2014).
(not an appellate case) said:
U.S. citizen’s right to reenter the United
States entails more than simply the right to step
over the border after having arrived there. At
some point, governmental actions taken to prevent
or impede a citizen from reaching the [border]
infringe upon the citizen’s right to reenter the
Even if we assume that citizens do not have an absolute right to re-entry, the Equal Protection Clause likely bars a religion-based criteria for citizen re-entry.
Citizens are protected by the Equal Protection Clause of the 14th Amendment. This prohibits the government discriminating based on a suspect classification (race, religion, national origin) unless such law passes strict scrutiny.
Without making a prediction about whether such a hypothetical statute could pass strict scrutiny, I'll go as far as I can and strongly guess that the government could not prohibit citizen re-entry to the United States based solely on their declared religion.