we looked at it from a linguistic background. Non means to not, but de means "Undo a specific action". Hence the non and the de prefices undo each other, hence the confusion. We don't speak english as a first language, so we rely heavily on Latin and Greek to figure out what a word is meant to mean
I am no expert, but Nominate may not be the root form of Denominate.
Nominate definition
specify (something) formally, typically the date or place for an event
Denominate definition
call, name
To be denominational is thus to "name" your sect. This name defines a set of believes or particular perspectives held by the sect, regarding the overarching religion.
Being non-denominational is to "not call, not name". In essence, to not declare the name of the sect.
Maybe in this case you should rely on English speakers
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