I'm pretty sure they call themselves agnostic, meaning one who believes that it is impossible to know whether there is a God or one who is skeptical about the existence of God but does not profess true Atheism.
I'm not sure that words like agnostic and atheist work completely. The question asks about a person without religion, which is a practice. It is altogether possible for someone to believe in the deity and not be practicing a particular religion. Unchurched may be a word that comes closer to actually meaning a person without religion.
Another word for religious group could be "faith community" or "religious organization."
'Dogma' is religious doctrine.
"Hymns" is another word for religious songs starting with the letter "h." Hymns are traditional religious songs typically sung in churches or during religious ceremonies.
smart ... or secular
Church, or culture.denominationreligionsectordercultdiocesestakeparish
sacriligious
Schism or sectarianism can be used as alternative terms for religious divisions.
congregation
pilgrimage crusade jihad
Religious tolerance or Religious toleration.
A group of religious people is often referred to as a congregation, parish, assembly, or community.
Someone who is religious believes in the tenants of their religion and considers religion important in their life. Other words for religious are devout, faithful, and pious.