In many Western countries, people can wear headgear, facial restrictors, and beards when other members cannot, why do we allow two types of citizens? I should be able to wear a ball cap regardless of my religion, wherever I want - it is my body. Why does a person have to profess a certain belief in order to grow a beard in the military? Why can't I have a beard because I want to? This stratification can cause strife in the workplace. There is an easy solution - give everyone the right, regardless of religion.
A US person recently won the right to wear a spaghetti strainer on his head for a passport photo, but had to say its because of his religion. A US army doctor got the right to not have to cut his hair, wrap it in a turban, and grow a beard but had to claim religion. What you are saying about forcing people to abide by standards is hard in Western democracies in the private sector, but easier in the public (ie govt) sector. In Quebec, the Charter of Values was proposed that would do what you suggested in the public sector and require anyone receiving benefits to unveil themselves when receiving. This can cause religious freedom issues that can be better resolved by immigration reform if people wish to have more uniformity, IMHO. I may find the idea of an eye ring (made up, I hope) horrible, but if there god Ow-Iris commands them to do so, any country that has freedom of religion cannot easily stifle such.
You can have every right to wear religious clothing, or any clothing, in your daily life. However,for professional matters, a certain image must be upheld.
Those in the military should abide by the uniform standards, those in government should abide by dress standards, and those in any professional setting should abide by the dressing standards set by their employer for the company or organization's image.
I can see your argument in a free market setting. If I do not follow or agree with company A's dress standard, I can go to company B, etc. For the military, a person who doesn't agree with their pre-1940's mandatory haircuts could join a security contractor for overseas operations (read: mercenary under international law). The problem with this notion is that the ideal look for a man or woman can be shaped by certain segments of society. This then trickles down, up, or laterally to the rest of society. Remember girdles? It used to be the standard that all women of proper upbringing would wear one. If a man did not have a beard after he was either married or in his 30s, he would likely have trouble getting a job or being taken seriously at certain points in history. This standard is still upheld by the Amish to some degree. By setting societal uniform standards, we take away the ability to create a new style or get rid of a bad one. With uniform standards, we may never have had t-shirts (at least for outer wear), jeans, not having to wear hats outdoors (look at pictures from the 30s - everyone wore hats outdoors). A loose societal pressure, such as is present in Japan and South Korea, would allow a change of style without necessarily causing strife. The loose societal pressure though may not be strong enough to not have religious exemptions.
The standards on society's dress is out of control of any government regulation, and trends will always come and go. Like I said in my last argument, you can wear anything you desire in your daily and personal lives in the social setting, these trends and normalities are set by your peers and the majority population.
In a professional setting, let's continue with the military example, you need to convey an image of discipline and order. These standards are also affected by the social norms. In our current society, a man with short-cut hair and a clean shave gives off an image of authority and order. In a corporate setting, a clean shave and a clean suit convey your image of professionalism.
Any mandatory dress standards are set to convey a good first-impression for the organization. Wether we admit it or not, we all judge each other based on what we look like. Much like in the justice system, a jury has an idea if the defendant is guilty or innocent just by looking at them.