@Dicrostonyx
Rules of grammar are social, communal, and cultural.
Things which are 'social' and 'communal' are often subjective. Your 'society' and 'community' may not be mine, and mine may have different 'rules'.
One of the truths about English is that it has no rule-setting body. It has multiple style-setting bodies, but there is no authority which can say 'this is the rule' aside from 'usage'. 'Usage,' however, can vary significantly over decades.
One can dance around this by saying that 'grammar' is reserved for a very small number of significant 'rules' and everything else is 'style,' but most people will differ with you.
For instance, your own definition includes 'Things like adjective order, verb placement, use of pronouns and plurals, how subject-object order changes tone, and so on.' I agree about adjective order. Verb placement is more complicated; English can be tolerant of some very unusual verb placements.
Use of pronouns, however, is clearly 'subjective'. For hundreds of years, 'they' was a perfectly appropriate gender-neutral pronoun. For a brief period in the 20th century, many 'grammar' authorities declared it to be inappropriate. More recently, it's returned to being considered appropriate, except for those who were influenced by the mid-20th-century grammar 'authorities.'
There are many other concerns. For instance, some people think split infinities are a violation of grammar rules, while some others think they're a violation of style rules, whereas many authorities on both fronts argue that, in fact, there is no rule against splitting infinitives at all, whether as grammar or style.
There is certainly a very broad cultural set of guidelines which constitute 'grammar,' but what that is is either necessarily very minimalist, concerning only the very basics, or instead subjective, because once one gets outside the basics, one finds there's room to differ on any number of points without compromising readability.