These are elected officials, conducting business meetings. Of which their constituents must play a part. 
They are there to do the PEOPLE'S business, not God's. 
Are the prayers from one denomination? Would you, if you were a Jew, Muslim or atheist feel comfortable, declining to pray? Or as a Catholic participate in prayers by a Mormon, Baptist or 7th Day Adventist? 

Again. Those who work in the public sector or provide services to the public need to follow the law.
No one if forcing them to change their religious beliefs. Or marry a gay person.
And I cannot believe that when they die, if asked, will be told, "no heaven for you for baking that same sex marriage wedding cake".
If you really believe that, then I can understand why YOUR world is upside down.
I hope that I can live up to and be judged by my actions in how I lived.
 Faith, hope and love. And the greatest of these is love.