Lots of people just know that the mistake of writing "your" when you mean the abbreviation of "you are" is depressingly common. But I'm sure that people who do make that mistake all the time know the correct version deep down. I think that if you told them that "you're" is definitely the shorter version of "you are" (of all the words in English) and that "your" is the word that implies second person possession, as in "the hat belonging to you, your hat", they'd understand it straight away.
I agree that these are the people who write "I should of" and who write stuff like this, on the BBC's Have Your Say page when Steven Gately died.

"hi like steve from boyzone and he is good and i like every one"
"i cant beleave came down da stairs dis morning and turned the tv on to the news channel to find out the weather for the day but the head lines said stevephen gately has died it is a shock to hear that such young man has lost his life but he has left a lot of memorys behind and he is the best singer as well and ronan dont talk hes hot hot but fear well to stevephen"

I know it doesn't exactly "look good". But do you really think that they would allow such overly casual sloppiness to show in formal writing (you can consider this post a good example of what I mean by that)? My parents seem to think they wouldn't know the difference between that and proper English. I hope that's not true...