Which law would be considered unconstitutional on the basis of First Amendment guarantees?

A prohibition on electing religious leaders to government office would be considered unconstitutional on the basis of First Amendment guarantees. This prohibition potentially violates the Establishment Clause and the Free Exercise Clause of the First Amendment, which together protect religious freedom and prevent the government from discriminating against individuals based on their religious beliefs when it comes to civic participation.

you sure

Yes, I am confident in that assessment. The First Amendment of the United States Constitution contains both the Establishment Clause and the Free Exercise Clause, which together protect the rights to freedom of religion and expression.

A prohibition on electing religious leaders to government office would infringe upon the Free Exercise Clause, which guarantees individuals the right to practice their religion freely, including the ability to participate in government and public life. Such a prohibition could be seen as discriminatory against those who identify as religious, as it would prevent them from participating in a democratic process purely based on their religious identity.

The other options you mentioned—such as bans on the publication of classified information by government employees, requirements for church employees to pay income tax, and requirements for churches to obtain permits for building—do not directly involve the same level of infringement on religious freedoms as a prohibition on electing religious leaders.

Therefore, the prohibition on religious leaders serving in government would indeed raise significant constitutional issues under the First Amendment.