I’d think almost everyone knows “they’re” is a contraction of “they are” and would select the correct word if they thought about it. When a person types their instead of they’re or it’s instead of its, it’s often just an aberration caused by typing quickly. Conclusions drawn about the person’s intelligence from something like this are likely to be very wrong.
I know this from myself. It’s been 55 years since I won a spelling bee but I test myself with games and puzzles and am not yet demented. However I frequently type wrong words, often completely wrong words that are phonetically a little similar. Among many many examples, I once wrote “vowels” for “values” and “pretends” for “protects.” I see evidence that some other Dopers make similar errors.
I don’t think it affects my speech much; I’m not sure about handwriting since almost all my writing is via keyboard. I didn’t have the problem when I was younger; it started in my 60’s. I find the way to avoid this and other typos is to stare at the keyboard while I’m typing, monitoring where the fingers actually go!