That is exactly what the First Amendment prohibits and the judge should be flayed.
This "praying in Jesus' name" thing has been an issue with the military chaplaincy for some time.
I decided that it's far easier to simply allow everyone to be him/herself. America is full of different religions and everyone knows it. It is not a secret.
So, if you have a prayer in a public setting, recognize the pastor/priest/rabbi/mullah you invite to pray should be himself. Otherwise, you're creating something that doesn't exist in the real world.
Also, it's a more adult view of the world. Lot's of differences out there. This judge should learn to live with that instead of trying to make all the ducks in life line up in his personal rows.