What's a word to describe people who blindly follow their government without question?

Solution 1:

While not a noun, the term knee-jerk is often applied to the category descriptor to demonstrate blind allegiance

(Of a person) responding in an automatic and unthinking way: knee-jerk radicals

[ODO]

Possibly partisan

a person who takes the part of or strongly supports one side, party, or person; often, specif., an unreasoning, emotional adherent

[Collins]

The term chauvinist is also used to indicate fierce commitment to a cause or point of view

A person displaying excessive or prejudiced loyalty or support for a particular cause, group, or gender: what a male chauvinist that man is

[ODO]

When coupled with an aggressive, often militaristic stand, the term jingoist may be used

Extreme patriotism, especially in the form of aggressive or warlike foreign policy.

[ODO]

Solution 2:

Sheeple is an interesting portmanteau that is a widely accepted term. An equivalent synonym/doctrine is "conformist."

[Sheeple] is used to describe those who voluntarily acquiesce to a suggestion without critical analysis or research. _^Wikipedia

It often portrays criticism in the tendency of crowd thinking and hive mindset. Here is a neat (perhaps very satirical) comic from xkcd to consider:

Solution 3:

I think you have already answered in your question by yourself, - 'a blind follower.

Solution 4:

A Yes-man :

a person who agrees with everything that is said ; especially : one who endorses or supports without criticism every opinion or proposal of an associate or superior.

Extract from http://www.lemauricien.com/article/political-fiction-yes-man

Elected in the same constituency as the Leader, the Yes Man is an expert in menial work. He started by carrying posters for a former banished young stud of the same faction. Despite being relegated to the sidelines, this has-been has managed to feed off the generosity of the party by aligning himself with another fervent patriot and organising PR coups where he gets to promote himself more than the real talents. However, let us not wander too far from our luminary presence.

Solution 5:

If such a person is actually part of the state, then they're a functionary or (more strongly) apparatchik. Allegorically, they are a drone or myrmidon, both words with connotations of insect colonies.

Otherwise they would be a zealot, true believer, or partisan who had drunk the Kool-Aid (referring to the use of poisoned Kool-Aid (Flavor-Ade) in the Jonestown cult mass suicide / murder).