The Oxford English Dictionary philosophy was always to document. So it has -ise and -ize as well as grey and gray. That's to say it reflects usage.
But Noah Webster was prescriptive and unilaterally decided to ditch doubled ll (jewel -> jeweller) and drop -our (to -or) and -re (to -er). American practice is like that ever since including an over emphasis on Latin roots of words and homonyms in primary education. Naturally the more prescriptive USA aspects are too rare to be adopted in the single volume Oxford dictionaries. Thus USA spelling and dictionaries are prescriptive, like a sort of English-American version of the Académie Française. The French that like the Académie Française don't like Canadian-French!
In the USA you might get marked down for using the wrong grey/gray in University. It would be ignored in a UK university, though maybe not at school. One is more common as colour and the other as a name. Both have been used in the UK for colour (commonly grey). Allegedly gray is preferred in the USA.
You can make up your own style rules to an extent, but spelling is either USA or not, unless you are writing "Clockwork Orange".
Grey vs Gray:
https://en.wikipedia.org/wiki/Grey
Spelling:
https://en.wikipedia.org/wiki/Americ...ng_differences
(Not entirely accurate!)
In practice – apart from the single "l" instead of "ll", "-or" instead of "-our" and "-er" instead of "-re" – the non-USA British, Irish or (ex-)Commonwealth reader often is familiar and might use the less common variant. My experience is that USA readers are only forgiving if the entire book is British English and USA Publishers & Institutions expect strict USA spelling in USA books and papers.