The part in question reads "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof;" (The rest of the sentence deals with non-religious matters such as free press.)
The two viewpoints basically boil down to who/what gets the legal rights. Conservatives see it as a right of the church, while liberals see it as the right of the people.
Conservatives generally describe it as a fairly limited restriction. That is their can be no 'official' establishment of religion, but 'unofficial' promotion is fine. Atheism is not a religion and get's no protection. You can ask people to pray as long as you don't force them to pray. Effectively, they want to guarantee the rights of each church to worship as it chooses, with no specific church gaining any advantage. Note that they leave open whether temples and mosques get the same protections - this lets some conservatives think "they don't", while others realize the constitution gives no special advantage to christian religions.
The liberals see it as a more sweeping. They don't allow 'unofficial' establishments of religion, atheism is protected as you can't force people to believe in a religion. You can't even ask kids to pray. Effectively, we want to guarantee that the government will not persecute people because of what we believe. We specifically include all religions, even atheism.
The current issue is slightly odd. Obama is not restricting religions or religious people. Instead he is restricting businesses and charities owned/run by religious organizations that have non-religious employees and serve non-religious people.
SCOTUS (Supreme Court) has said that the government can make reasonable non-religious based laws and people can NOT use religion to allow them to break the law all the time. But special exemptions are allowed for religious ceremonies. Specifically, a member of Native American Church can not grow, sell, buy or use peyote for personal enjoyment, but they can do so for a religious purposes. They must be registered and follow the law.
Religion gets special exemptions - but ONLY for religious purposes. This is something that conservatives agree on. If you ask them if an American Indian can legally sell peyote to their kids, they will say no. But for some reason they don't want to extend that same idea to christian organizations.
The real problem is what happens when a religion deliberately blurs the line between it's religious activities and non-religious activities? Churches have gone into a LOT of non-religious businesses and charities. Private schools, wineries, hospitals all are owned by churches. Not just the catholic church - The Church of Latter Day Saints (Mormons) own 3 universities.
Now these people are tring to use religious exemptions for their BUSINESSES, as opposed to their religions.
Here are 7 situations, stripped of some of the confusing stuff, of 7 different levels of religious hiring.
- A catholic priest hires cleaning person to clean the church.
- A catholic priest hires an atheist cleaning person to clean the church.
- A catholic priest hires atheists to run a charity to give to destitute nuns.
- A catholic priest hires nuns to run a charity to feed the homeless (of any religion).
- A catholic priest hires atheists to run a charity to feed the homeless (of any religion).
- A catholic priest hires atheists to sell wine he made.
- A catholic priest buys 51% controlling interest in a winery.
Obama's position is that in situations 1-4, the church doesn't have to buy insurance that includes birth control, but in 5-7 it does. If you are employing non-believers to serve non-believers, that's no longer a religion. You can't force them to convert to your religion and you lose most of your religious exemptions.
The Church's position is that they never have to buy insurance that includes birth control. Not even if the priest doesn't completely own the business. Mainly because they don't care about the law, they care about what their religion says.
At heart the conservatives see it as the church having the right not to pay for something it doesn't believe in. The liberal view is that the church can not willing hire non-believers to do non-religious activities then say "Oh, but you have to follow our religion in your personal private life". That's not fair. You can't force your religion on other people - even if you employee them.
Given Obama's new ruling, where the insurance company is not allowed to charge a different amount of money for insurance that doesn't cover birth control. Now, it is the insurance company's money that's paying for the birth control, not the church's money. So the church's are complaining about how a vendor they use is being forced to ignore the church's beliefs..
Without the insurance then the church pays the employee and the employee pays the bill. With the insurance, then the church pays the insurance company and the insurance company pays the bill. Either way, if the employee decides they don't agree with the church and wants the birth control, the money starts out with the church, goes through one intermediate and ends up being used to buy the birth control.
The question becomes should the church in effect be allowed to force the employee to take a minor cut in pay if they use their right to birth control or should instead the insurance company be allowed to take a small profit extra if the employees choose not to use their right to birth control?
The CHURCH that is trying to pull one over on us. The government is being neutral. Note we are not talking about the church paying for religious activities. We are talking about a church running a separate non-religious business - such as a winery (or a hospital or a charity for homeless), hiring athiests, mormons, muslims and jews.
Churchs are tax free. Business owned by a churches are not. The further you get from religious activities, the fewer religious rights you get. When you lose your automatic tax free status, you lose the right to object to activities that your religion objects to.
When the church hires non believers to do non-religious activities, it must obey the laws of the country. If they can't, then don't do businesses.
Which is probably why most Catholics agree with the president.