I do not see any evidence that fundamentalism has a religious connotation, except that religions are more likely to bear fundamentalists than paradigms that are to some extent based on empirism or argument. For example Merriam–Webster defines fundamentalism as follows:
a often capitalized : a movement in 20th century Protestantism emphasizing the literally interpreted Bible as fundamental to Christian life and teaching
b : the beliefs of this movement
c : adherence to such beliefs
: a movement or attitude stressing strict and literal adherence to a set of basic principles <Islamic fundamentalism> <political fundamentalism>
The first definition is religious, but pertains to a specific religious movement and would also exclude, e.g., Islamic, Hindu, or Judaist fundamentalism.
This second definition already gives the example of political fundamentalism, which is not religious. Other non-religious usages that I found in a brief search include: market fundamentism, secular fundamentalism, materialist fundamentalism, Marxist fundamentalism, communist fundamentalism, left-wing fundamentalism, ecological fundamentalism, national fundamentalism, and Chicago fundamentalism.
The main difference of fundamentalism to what you want¹ is that there is no restriction on the source of the principles of the fundamentalist movement, while in your case, there is some sort of authority. So, it’s a little bit broader (unless you a set of principles qualifies as an authority).
¹ “the belief that there is a single or narrow range of correct interpretations of events or a circumscribed set of permitted actions in a particular situation as prescribed by an unquestionable authority”