Yes, religion plays an important role in contemporary society, because it helps people find a reason to do well in life. Many people take their moral compass from religion. Their God tells them to obey laws and help other people so that is what they do. In that way, religion plays an important role keeping society civil.
Religion still plays a more important role in contemporary society. This is because it is the end all for all decisions in people's lives. Most political views can be traced back further to religious views. I don't agree with people relying on religion as a crutch to make decisions but that is still has society operates.
I believe that government plays a more important role in contemporary society, at least in the United States, it does. When church and state separated, people grown accustomed to religion or religious tenants not being enforced, while governments law were strictly enforced. As time has passed, it has become more important to follow the rules set out by the government, rather than the rules set out by the church.
More and more young people with their impressionable minds are shunning organized religion and turning to each other and technology for stimulation. Especially in nations like America and China, more kids have more things to do like sports, Scouts, extracurricular activities and homework so much so that religion gets pushed aside. Add college to that list and our society gets even more secular with less organized religion. Many Christian churches face a population decline because young people are abandoning churches to get ahead in life. So I would say government plays a bigger role in contemporary society now as traditional religions aren't changing with the times.
Government can be seen as playing a more important in contemporary society.While every citizen does not attend church on a regular basis,each citizen has contact with the government on virtually a daily basis.The government is involved in a person's life from cradle to grave and even after the fact many times.