Fascinating stuff..When I see “your going out” it doesn’t phase me because it sounds the same when I read that sentence to myself. I notice it, but it doesn’t matter.
On the other hand misspelling big words is different. Well, for small words I’m not fond of people misspelling “friend”. You quite often see “freind”. It’s not a big deal, but I’m more inclined there to think, “shouldn’t you know that word by now” – than when I see “your going out”. With the latter, most likely it’s a genuine mistake, because someone typed too fast. It could happen to me too. But then I’d feel odd going back and saying “sorry, I meant you’re” because I know – you know what I meant.