Clarifying the First Amendment

"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..."
This is probably one of the best known lines in the Constitution.  It is also one of the most poorly understood.
There is a case before the Supreme Court now.  Two women in upstate New York are suing to ban a blatantly Christian prayer that opens a public meeting.  The women, one Jewish, one atheist, state that being forced to participate in the prayer when they attend the meetings on other business infringes on their First Amendment rights.
Let's break down that famous line from the First Amendment.
What does "prohibiting the free exercise of religion" even mean?  It means that whatever your faith, you are free to practice it as you so choose.  If you wish to cover your eyes and say the Shema twice a day, you may do so.  You may burn incense in front of a golden Buddha.  You can attend church and light candles to the Virgin Mary.  You can say "There is no G-d but Allah and Mohammed is his prophet" with complete sincerity.  You can cast a circle in Central Park on October 31st and invoke Hekate.  You can join the Church of the Flying Spaghetti Monster.  I don't care.  And neither does the US Government.
What you may not do is force me to join you.  And that's where the whole "respecting an establishment of religion" comes in.
If a hundred very devout Christians want to start a prayer club in their public school, they may.  They may not, however, insist on leading the Lord's Prayer before algebra class.  And it's the same thing here.  Go to church and pray for the welfare of the government.  But a town hall is not a church.  And a government meeting that people need to attend for business is not the place or the time to pray to a deity.  Why?  Because you're essentially holding those who do not share your beliefs hostage.  And that's not OK.
There are those who say that the US is a Christian country anyway, so let the prayers continue.  But what if it wasn't?  What if we were majority Buddhist, and every government meeting included lighting incense in front of a golden Buddha?  Those whose faiths prohibit idol worship would be outraged.  Similarly, what if we were majority Rastafarian, and every meeting included passing a bowl for a ceremonial smoke?  (Although that would make government meetings more interesting...but I digress.)
We need to remember the old rule that our rights stop at someone else's nose.