Is there a word for someone who doesn't follow unspoken rules?
Example: You do not yell in a movie theater during a movie. This is not a "rule", but it should not be done for it is just plain rude.
It's very pejorative, but social misfit might suit. From Collins Dictionary:
social misfit noun
a person who does not conform to others' views of what is normal or acceptable in society
- He was shy, but not a social misfit; he had held down a senior position at the Welsh Office.
I think the "what is normal or acceptable in society" part of the definition corresponds fairly well with "unspoken rules". These are often called social norms (see, e.g., Oxford Reference) so a more clinical term could be nonnormative, in the sociological or social sciences sense (see Wikipedia for more on this specific usage of normative).
Depending on context, I'd call them "boorish", though it is not specific for those who ignore unspoken rules".
from MW - - "resembling or befitting a rude or insensitive person."
boorish implies rudeness of manner due to insensitiveness to others' feelings and unwillingness to be agreeable
boorish behavior, such as yelling for service in restaurants
"Maverick" is not quite right. A maverick is, say, someone who dyes their hair purple. It's someone who knows how things are supposed to be done, and does them differently anyway, but not to the extent of seriously imposing on someone else. (The word originates from a term for a cow in a herd that is unbranded). A maverick isn't rude.
A "boor" is someone who imposes on others by ignoring social rules. Yelling in a theater is boorish behavior.
From the Merriam-Webster dictionary -
a person who refuses to follow the customs or rules of a group
I think this definition is particularly apt because when you asked about 'unspoken' rules you are, in a way, referring to social norms or customs, so the term maverick seems apt.
Bearing in mind that you want to express the idea of being antisocial, it seems you want a pejorative word.
Informally, there are a series of strong, offensive, oaths: "cunt, twat, nutter, etc." that are general words for someone who is a great annoyance and/or antisocial.
On a more socially acceptable scale, there is "idiot, troublemaker, loudmouth, arse/arsehole," and probably a few others.
In practice, the idea that you want would be expressed by descriptive phrase that gives some indication of the nature of the offence. As such, there is no single word.