A country can have an official religion but otherwise is a geographic entity. Only people have religion. A country isn't a person.
At least these countries and should be more have no state sponsored religion:
United States, Australia, Canada, People's Republic of China, India, New Zealand, France, Japan, Columbia, Chile, Ireland, Azerbaijan, Czech Republic, East Timor, Nepal, Netherlands, Nigeria, Philippines, Portugal, Republic of China, Romania, Singapore, South Africa, South Korea, Switzerland, Republic of Turkey