The Center for Inquiry has filed a federal lawsuit challenging a law in Indiana that forbids secular organizations and individuals from performing legal marriages, reserving that power for clergy and certain elected officials only. You can read the full complaint here.
The ACLU of Indiana is representing them in the suit and they provided a press release about it:
“From a First Amendment perspective, it is proper and necessary for the state to allow religions to marry
people according to their beliefs,” said American Civil Liberties Union of Indiana Legal Director Ken Falk. “However, the state law becomes unconstitutional under the Establishment Clause when you say that religions are the only groups with rights to have their beliefs recognized in marriage ceremonies.”
Falk said the statute, Indiana Code § 31-11-6-1, also violates the Equal Protection Clause of the Fourteenth Amendment because it denies the non-religious group its rights to spread its “essential beliefs” by performing marriage ceremonies, while allowing religious groups those same privileges.
There’s a similar case going on in Nevada.