The important thing to remember is don’t use possessive apostrophes with any pronouns, either possessive pronouns or possessive adjectives.
If you see an apostrophe with a pronoun, it must be part of a contraction.
its—possessive adjective of it
it’s—contraction for “it is”
The nature of the object doesn’t change which form to use (which should make it easier to determine which is correct), and the correct form is not a debate.
Sure, language changes, but for now that’s the accepted rule.
We both used links from the same source.
I’ve traditionally used no apostrophe for inanimate objects, like a bus.
But when dealing with a gendered, thinking being, use the apostrophe.
Edit: no need for down-votes for a good-faith discission, is there?
Downvotes for spreading incorrect information is appropriate.
From the page that you linked:
The nature of the object doesn’t change which form to use (which should make it easier to determine which is correct), and the correct form is not a debate.
Sure, language changes, but for now that’s the accepted rule.
Can’t tell if troll or tragically clueless