In the context of religion, the strictest adherence to traditional beliefs is called:

It is called "fundamentalism".

Fundamentalism for the most part has a religious implication that demonstrates steady connection to an arrangement of unchangeable convictions. Fundamentalism was utilized at first to portray a few people in the Protestant community in the US in the mid twentieth century. These individuals had an arrangement of very much characterized ("fundamental") values. These qualities were contrary to more current thoughts.