To have a clear understanding of the role religion should play in peoples lives, both public and private, I think it is necessary to determine what religion is.
The Dictionary definition of religion is; "the body of persons adhering to a particular set of beliefs and practices."
Working with this definition it would be impossible to separate religion from any one's life, public or private. Even those who claim to belong to no 'religion' would still have to admit that there are certain things they believe and therefore practice. It could be said with almost certainty that everyone believes they are alive. So, they are adhering to that particular belief and living there life accordingly.
A much more narrow definition of religion is; "a set of beliefs concerning the cause, nature, and purpose of the universe, esp. when considered as the creation of a superhuman agency or agencies, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs"
This narrows things down quite a bit. After all not everyone is involved with "devotional and ritual observances". However, does this mean that people that claim to belong to no religion are free of any system of beliefs? Certainly not. Everyone believes in something. So, why would the individuals who choose to worship corporately or adhere to rituals and observances be singled out concerning there 'religion' in the public realm, as they so often are?
So, everyone has religion. Wither they are an atheist, Buddhist or Christian. Everyone believes in something. It is therefore, necessary that religion play a role in peoples' lives. It is therefore, unavoidable that religion will play a part in peoples' lives.