Is this because you are genuinely confused (even for a brief moment) as to whether the word is intended to mean "it is" vs. the possessive of it, or is this because the proper rule has been so ingrained into your mind? If the latter, perhaps the problem is the ingraining of a rule that should never have been ingrained in the first place?
It depends on what you mean by ingrained. I was taught the correct usage, I did not forget it, and I see no good reason to abandon it.
I'm not confused per se when I see the wrong usage, but the reason I'm taken out of the text is because I read 'it's' as 'it is' in my head (since that's what "it's" is).
Far more rare than the "it's" vs "its" error.
Not in my experience. I took a photo once of a sign proclaiming 'Tyre's deal's'. I see the mistake more often with nouns ending in a vowel (I bought two umbrella's at the shop, along with some salami's) but ending on a consonant is no barrier to apostrophe excess either (the magazine featured modern designs for bathroom's and kitchen's).
I can't speak to the apostrophe for a noun that is intended to be pluralized. At least the "it's" error makes some sense - the possessive form of a noun always has the apostrophe.
The possessive of a pronoun never has an apostrophe.
His bat.
The ball was hers.
Its quarterly profit report.