With bans on gatherings due to the virus, can the government close churches or are they exempt due to seperation laws?
The Free Exercise Clause of the First Amendment requires government restrictions on churches to satisfy a compelling government interest, such as preventing massive deaths from disease. The Establishment Clause of the First Amendment prohibits the government from granting special privileges to a specific religion or to all religions (Everson v. Board of Education, 330 U.S. 1 – government may not "pass laws which aid one religion, aid all religions or prefer one religion over another").
Exempting only religious gatherings (however defined) would be unconstitutional. Restricting all gatherings (including religious gatherings) would be constitutional (subject to the general restrictions being itself constitutional).