I think that the reason the government relies less on religious influences than in the past is because now people are more influenced by facts. For example I believe most of the united states is very influenced by facts, more so than religious experiences. However the level of influence from religion varies, there are many countries that are still very religious based, more so than facts.
Contrary to my previous statement the United States has been declared one of the most religious countries in the world. About 46 percent of American adults attend church at least once a week, not counting weddings, funerals and christenings, compared with 14 percent of adults in Great Britain, 8 percent in France, 7 percent in Sweden and 4 percent in Japan. The other country I can think of is in the middle east, Iraq and Iran are both very in tuned to there style of government and which of the two major (sunni & shiite) religions runs it. Cuba, Nigeria, and Saudi Arabia.
Separation of State and church
One of the advantages of having the separation of state and church is the balance of power. People living in the country run are not forced to follow one religion appointed by the government. The government did not have to base it’s decisions on what is right in the religion.
People are not all of one religion and some conflicts may develop. There less likely to support each other financially. The government had less control over people’s religious practices. Less holidays as a nation and more as personal celibrations.