[tacticalogic]

I mean a term that can accurately include such mutually exclusive beliefs, such as belief that man is the highest authority/intellect, and one that God is the highest authority/intellect. hardly gets to the truth of the main premises.

Okay. Now, does every instance of the term "secular" meet that criteria?

[flevit]

no
there are many usage of "secular" one is "through the ages", it would depend on the context and usage, in common usage with politics/policies, "secularism" implies the underlying belief that man is highest authority/intellect through declaration (atheism) or irrelevance, for practical purposes, there is not much difference with the premise of nonexistence or irrelevance, both still rely on men as final authority.

I hope that answers it but I wasn't sure on which "criteria" you were referring too.