The intersection of religion and politics is complicated, but not so complicated that we can't make some sense of it.
Some people think that "religion" means anything you want to call your religion. And while it is true that the heart of religious freedom is the right to believe whatever you want about eschatology -- the meaning of life, if you will -- this is among the least disputed aspects of religious freedom, and therefore the least interesting. No one will argue that you should have to convert to another religion to live freely in the United States. If you believe in the Church of the Flying Spaghetti Monster with all your heart, that is your right. If you are an atheist, that is a form of religion and no one will claim that you should be forced to believe in a god. They might wish you did, but I have not seen any serious arguments that you are required to do so.
But religion is not synonymous with whatever an individual believes about religion. "Religion" is a social phenomenon. You may have a religion that no one else shares; for example, you may believe that weekdays are holy and are intended for rest, whereas weekends are intended for work. No one will dispute your right to believe this. (They will likely dispute whether you are correct, but they won't deny your right to believe it.) The government, however, will not make many accommodations for your beliefs. If you get a job working for the government, you will be expected to come in on weekdays like everyone else. Anything else would be impractical from the government's perspective, and it isn't going to reorganize the way it does business around your beliefs.
The situation is quite different for people who, for religious reasons, prefer to work on weekdays and rest on one or both days of the weekend. Our work week is deliberately structured around their needs, and if anyone tried to change it -- for example, by shifting the workweek to a Wednesday-to-Sunday schedule and taking off on Mondays and Tuesdays -- he would be met with enormous opposition and calls of religious intolerance. And he would almost certainly back down.
This may seem a very un-spiritual way to approach religious freedom: why are people who practice mass religions and share similar beliefs allowed to influence public publicy in this way, whereas an equally sincere individual with different beliefs gets ignored? The answer is that it is not at all spiritual, and is really not intended to be (I don't think it is, anyway). It is a practical response to the fact that a large portion of society shares similar beliefs.
If you object, think of the consequences of allowing every individual view to influence public policy. Not only would it create chaos, as in the example of the scrambled work week, it would also allow anyone to apply the tag of "religion" to anything he happened to want, and who would be able to contradict him, since it is a matter of his own conscience whether he means it or not? And perhaps some people -- the most narcissistic probably -- would actually believe that their religion did require them to do things that happened to be in their own best interests. Society would be unable to function under such a system.
Another alternative would be that we could ignore everyone's religious beliefs and organize society with no account to anyone's religion. There are a couple of problems with this, however. First, who would choose the method of organization? Since we have defined atheism and every other ultimate belief as a form of religion, there would be no neutral person to decide what to do. Any organization would inevitably favour one set of beliefs over another, and that would lead to complaints and lawsuits and ultimately we would not be better off in the least. We would have to choose a system based not on a rational basis but on how to offend everyone equally, which is a fool's errand.
Second, any religion that contained a substantial membership would run afoul of the chosen organization and might refuse to participate. This might be to their own detriment, but beyond a certain size it would also be to the detriment of the government and the society. Things would be organized on two principles, one official and one non-official. Imagine if 80% of Americans celebrated Wednesay as a day of rest: how much government business would be conducted on that day? How effective would it be, since a lot of government action involves interacting with businesses and individuals, most of whom would not be willing to participate? The government would look silly for being open on a day when few people were willing to deal with it, and surely all sides of the political spectrum would call for taking Wednesdays off as a practical matter.
The poor individual finds no accommodation in this scheme. He must adapt himself to society rather than adapting society to himself. But this is the case for everyone who runs counter to society, whether on religion or economics or art or sports. We believe in your right to freedom of conscience, and you can act on your conscience how you will as long as you are not violating other laws. Government and society may make accommodations for you, but they cannot be organized around every individual's religion. The government does not take a holiday on Yom Kippur, but it is willing, I believe, to accommodate Jews on an individual basis if, say, a court date would fall on that holiday.
People seem afraid that religious freedom laws open the gates for everyone to claim anything he wants in the name of religion, but this is a fantasy. Hobby Lobby claimed a right not to be forced to provide abortifacients for its employees, a position consistent with centuries of Christian teaching and in accordance with the views of many other Americans. It is important that Hobby Lobby was already practicing its views when a new law required it to change. If it now claimed the right not to pay a minimum wage, what force would that have? There is no Christian teaching that I am aware of to support such a view, and even if they could bring forward a dozen Bible verses in their favour, that would not make it a Christian belief. Christian groups have evolved a set of beliefs over centuries and, while individuals are free to reinterpret them at will, it is not a government concern unless it falls within an established tradition. Hobby Lobby would have no case, and the people afraid that religious freedom would be used to avoid laws would have nothing to worry about.
For much the same reason, it is pointless to argue that a religion should not espouse a belief because it is not being true to its principles. It is quite legitimate, of course, to try to convince religious leaders to change their beliefs, but it is another matter entirely to claim that the religion's teachings are inconsistent with its background and therefore not subject to public accommodation. I have seen many articles in which liberals argue that the Bible is not unambiguously opposed to same-sex marriage, and therefore that religious groups should not be accommodated in their refusal to participate in same-sex marriage ceremonies. This overlooks the obvious fact that almost all Christian churches have consistently taught that marriage is purely a heterosexual institution. Even if the Bible contained verses that seemed to contradict this notion, it would not alter the historical belief of Christians. Public policy is not the place for a theology debate. I assure you that early modern Catholics were convinced that Protestants were reading the Bible all wrong and used this as a reason not to respect their religious beliefs. The situation was exactly comparable: they were not following the true Christianity, so there was no reason to allow them to practice their false beliefs. That did not work out in the end, and the attempt to do it now has the same fundamental problem (except that Christianity's teaching about marriage is much, much older than the Protestants' interpretation of Scripture in the 16th and 17th centuries, so the attack on it is even more tenuous).
The same things that protect us against arbitrary religious views on the part of individuals also protect us from groups claiming a place alongside established religions in public policy. There is no reason to believe that a government that makes concessions to one religion, such as Christianity, must make equal concessions to all religions down to the Church of Satan. While Satanists may be sincere believers, with progenitors going back centuries, there is no established tradition of a Satanist church prior to 1966 and very few members even today. If, in a hundred years, the Church of Satan comprises 2 or 3 million members and has a relatively consistent body of dogma, it may well demand and gain a place alongside established religions. I have no doubt that the Founding Fathers entertained no idea of religious toleration for Satanists, but that was because they did not exist, at least not as a movement. For the early modern Catholic Church, Protestant reformers were little better than devil-worshippers, yet they managed to reconcile to their co-existence eventually. They did not accept it until half of Europe had been Protestant for several centuries, and while the required longevity and spread of Satanism or other religions might be less today -- and while we would not burn them at the stake in the meantime -- there is a similar waiting period before it could be considered a religion worthy of accommodation in the public sphere.