In certain academic circles, it's been popular for several decades now to exhibit indifference to the general decline in observance of rules such as this. I find that attitude very regrettable. I can't be the only person who has found themselves having to repeatedly re-read a passage of text to discern its meaning, because the author is ignorant of, or indifferent to the use of apostrophes and/or other forms of punctuation.
These aren't arbitrary rules, for the most part: they came into existence to assist with reading comprehension. The clarity of expression afforded by modern English is a great gift, and I strongly believe that allowing it to degenerate by abandoning these (very simple!) rules will serve only to make written English less expressive and more opaque.
This particular case is probably not the best example, though, given that the lack of apostrophe for "its" is inconsistent with its use for possessive case for regular nouns in the same circumstances. If we really wanted to maximize readability, we'd use apostrophe for possession everywhere (including "he's" for "his") and use something else entirely to denote the contraction of "is" and "has" - preferably two different markers since these can also be ambiguous in many cases. Or vice versa, use apostrophe for contraction and e.g. hyphen for possessive: "it's" vs "it-s" etc.
My wife still fumes that they don't make kids type two spaces after sentence-terminal punctuation anymore. And she still hasn't processed that periods at the end of sentences are, in certain contexts, considered inappropriately arrogant and to be avoided.
FWIW I think that anyone who seriously believes this needs to be told to just go fuck themselves, so if they choose to treat such style as "rude" and get offended, perhaps it's for the best after all.
These aren't arbitrary rules, for the most part: they came into existence to assist with reading comprehension. The clarity of expression afforded by modern English is a great gift, and I strongly believe that allowing it to degenerate by abandoning these (very simple!) rules will serve only to make written English less expressive and more opaque.