It’s pretty well-settled law in California that invocations used to open government meetings must be non-denominational. That doesn’t mean city councils follow the law, but that’s the law.
That question may be a bit less answered in Minnesota, where a Jewish legislator is asking the state Senate leaders to only allow non-denominational prayers. The AP reports:
Terri Bonoff, a Jewish Democrat from Minnetonka, a Minneapolis suburb, said: “We honor God in public and our political discourse, and that’s proper. But in doing a nondenominational prayer, we are honoring him without violating the separation of church and state.” Amy Koch, the Republican Senate majority leader, in rejecting the requirement, said the Senate invited leaders from numerous traditions to pray. “I’m not going to get into the process of sort of editing prayer,” she said
It’s not really a matter of editing but of having guidelines that ministers are told to follow.