Word like culture, but specific to an individual?
In my book
It might not always fit what you're trying to express, but should do most of the times. (I would also like a better answer.)
Examples:
In my book, if I lend you something, I should not have to ask for it back.
And to quote Google Definitions, that counts as a lie in my book.
Greybeard's answer mentions the word ‘standards’, and I think that may be a good answer in itself.
“By my standards,…” you might say, or “According to my personal standards,…”
It's clear and likely to be universally understood. It also highlights (which the question does not) that these issues loosely concern matters of personal morality — what is acceptable and what's not — unlike ‘culture’, which is why that's a bad fit.
‘In my world...’
Is the expression I use myself, for exactly this.
It denotes that ‘my world’ is indeed, personal.
It allows that another person’s ‘world’ might be very different and is also - personal.
And it lets me posit ‘a way of being’ or ‘a perspective’ in that ‘individual world’ which although it might be quite controversial or avant garde for the person I am talking to - becomes then ‘a possibility, choice, or optiom’ - rather than being ‘a threat’ or ‘offensive’, allowing me to suggest a new idea or a new way of being gently and without treading on anybody’s toes.
I am an intuitive healer, I delve into very deep areas of my clients’ ‘personal culture’ all the time, relating to sub-conscious belief systems (which are, in my world, what define people’s ‘personal worlds’) and this little invention of mine, helps me a lot!
https://dictionary.reverso.net/english-definition/in+my+world