To elucidate a bit: I'm trying to find a word that means believing strongly in something and expecting others to believe in it as well. I've found words like "domineer" and "proselytize", but the difference there, as I understood it, is that those rather focus on the action itself of asserting one's will; what I'm looking for is more something like having a belief, not consciously enforcing it, but judging and criticising others for not thinking the same way. Is there such a word?
Presumptuousness is a reasonably close match that would work in many related contexts, though a hypernym. The adjective is defined at YourDictionary:
presumptuous: too bold or forward; taking too much for granted; showing overconfidence, arrogance, or effrontery.
presumptuous: overstepping due bounds (as of propriety or courtesy): taking liberties
There are already threads covering 'unwilling to change' / 'hidebound'.
projection - the attribution of one's own ideas, feelings, or attitudes to other people or to objects
This isn't it entirely. I have not had luck finding a term for the logical fallacy of building an argument upon projection of one's own attitudes to others. Maybe projection combined with argumentum ad populum.
How about "prejudice[d]"?
From dictionary.com, the #2 definition of prejudice (noun) is defined:
any preconceived opinion or feeling, either favorable or unfavorable. (link to dictionary.com — "prejudice")
while the most common verb usage, prejudiced, is simply an act of applied prejudice. More commonly you'll encounter the identically-spelled adjective form (https://www.dictionary.com/browse/prejudiced). (But technically there is also an irrelevant legal verb usage, which is not the usage I'm suggesting.)
It's a bit ambiguous in your question whether you are describing an actual act (i.e., a conscious decision to take an action) or arguably a phenomenon of the mind and thus perhaps better articulated in noun form — "prejudice" [of the mind]. It's not a verb because it's an affixed, immovable opinion trapped in one's unconscious(?) Debatable!
(quite obviously) indeed suggesting "pre[liminary] jud[gement]" about something; with the quoted defined usage of the word given above further implying that the preliminary judgement(s) have already been "preconceived". That is, they are so strongly believed that they are deeply engrained — reflexive acts, thoughtlessly＊ held expectations.
(＊There is no action; but rather a constant expectation, a thing, held as personal conviction and "thought to" oneself in private so resolutely that no further thought on the matter even occurs now, in actuality – though typically when confronted with prejudice, the receiving side is deceived or attempts at deceit are made to pretend that actual thought on the matter has occurred.)
Hence there is a flair of negative connotation to the word prejudice of course, in that there's rarely a non-evil motive which originally seeds it. But, I assume you couldn't possibly be looking for an entirely positively connotated word, judging by the undertone of your question, OP. However, I suppose that may be prejudiced of me!?
...what I'm looking for is more something like having a belief, not consciously enforcing it, but judging and criticising others for not thinking the same way.
This way of thinking is characteristic of a self-important person.
Having or showing self-importance m-w
An exaggerated estimate of one's own importance : SELF-CONCEIT m-w
A sense, esp. an exaggerated one, of one's own importance; behaviour or an attitude originating in or expressive of this; conceitedness, vanity OED
Left unchecked, this protectionism can build into a false sense of self-importance, so much so that you may believe you have the right to expect others to allow your actions and beliefs precedence over everything and everyone else. D. W. Freeman; Sow Right: (Re)discovering Purposeful Living
Another person may lack a sense of humour because of his self importance. Such people take themselves too seriously. ...
In some cases they are quite ready to laugh at other people and criticize them because that raises their self esteem. J. Hadfield; Why Do We Laugh
Narcissists have an exaggerated sense of self-importance. They believe that they are superior to others and are unable to recognize other people's feelings. They expect others to go along with their ideas and plans. Finlay MacRitchie; The Need for Critical Thinking and the Scientific Method
Has a grandiose sense of of self-importance (e.g. exaggerates achievements and talents, expects to be recognizes as superior without commensurate achievements). Jerrold Post; Leaders and Their Followers in a Dangerous World
Such self important sacred men utter oracles, which they expect their hearers to receive with reverence, and they are offended when their hearers doubt what they affirm. G. L. Walker; The Idea of Being Free
At the same time, however, it is hard to overlook their rather self-important view that everyone will obviously agree with their selections. C. Bloom; Literature, Politics and Intellectual Crisis in Britain Today
And anyone who expects the entire world to adjust to them is obviously a little too full of their own self-importance. John Klima; Happily Ever After