For most religions, relies services are serious formal events held in traditional locations. For these services, your clothing should match. This means it should be formal, rational, conservative and clean-cut. Business Casual clothing fits all of these requirements.
For men, at a minimum the dress code for a religious service typically involves wearing a plain dress long-sleeved dress shirt, dress pants and dress shoes with a matching sport coat. For some religions and denominations (especially in the spring and summer), less formal clothing including lighter colored khakis and brown shoes may also be appropriate. That said, it's best to check with the place of worship ahead of time to ensure you are dressed appropriately
You can never dress too formally for a religious service - someone will always be dressed in a suit
Some religious occasions may call for wearing a certain color or clothing item
Keep in mind that you may need to kneel down for some religions - choose clothing that allows you to do so