Word for someone who blindly follows a religion or government

One obvious contender is fanatic, and the related adjective fanatical:

NOUN

1 A person filled with excessive and single-minded zeal, especially for an extreme religious or political cause.

EXAMPLE SENTENCES

Much to the chagrin of my room-mates, come election time I will roam around extolling the necessity of voting with the zeal of a religious fanatic.

The extreme right wing religious fanatics truly scare me beyond belief.

Wesley's eyes glint with a religious fanatic's zeal.

(Definition and examples from Oxforddictionaries.com)

You could also describe such a person as a slavish adherent / slavish supporter [of something].

I think you might have been looking for "ideologue."

https://www.merriam-webster.com/dictionary/ideologue Definition of ideologue 1: an impractical idealist : theorist 2: an often blindly partisan advocate or adherent of a particular ideology

The word "devotee" is suggestive of unwavering (and perhaps quasi-religious) personal commitment.

acolyte (originally one who assists a priest, but later a follower)

MW lists synonyms as:

follower, adherent, convert, disciple, epigone, liege man, partisan (also partizan), pupil, votarist, votary

APPARATCHIK

A word I have not heard in many years but that I believe applies to many in our current political climate (garnered from Merriam-Webster online) :

In the context of the definition of "apparatchik" (a term English speakers borrowed from Russian), "apparat" essentially means "party machine." An "apparatchik," therefore, is a cog in the system of the Communist Party. The term is not an especially flattering one, and its negative connotations reflect the perception that some Communists were obedient drones in the great Party machine. In current use, however, a person doesn't have to be a member of the Communist Party to be called an "apparatchik"; he or she just has to be someone who mindlessly follows orders in an organization or bureaucracy.