English teacher reporting in:
The most important thing to note is that, in my experience, nothing has really changed from how it's been since I was born. The only difference is now grammatically-poor people are able to be more vocal. They've always been there; you just didn't see them.
Secondly, the type of person who posts on forums and reads constant online discussions is not your average person. You are more likely to be linguistically-focused than your average person who spends all of his/her online time viewing videos and memes.
Another major player in the game is spelling/grammar-check. When a person grows up with software correcting mistakes, the lack of skill really shows itself when a less-effective correction algorithm comes into effect.
I have also spent a lot of time teaching 18-year-olds how to capitalize certain letters. When you consider that 50% (or more) of people are below your skill level, if you were a C-student or better, that really makes you realize just how many people out there are quite pathetic at something you find relatively easy (even though you might suck at something they find easy).
I've heard two separate thoughts on the issue: 'You must follow the rules, and breaking the rules is incorrect;' but also 'If I can understand you and the message gets across, then there's no such thing as right/wrong.'
And so I come to my thoughts: I like to separate spoken language from written, even though it makes the whole situation more complex.
With spoken language, it's very easy to understand people, even if the language is nowhere near correct regarding traditional grammar rules.
With written language, it's much more difficult. There is absolutely a point where too many mistakes can make the meaning get lost in translation. If a person doesn't adhere to specific, basic, rules, that person might as well be a moron - no matter how interesting the idea may be.
But the real issue is with reading-comprehension.
Ignoring certain rules isn't all that big of a concern with how things are written; the real concern is with how things are read.
Think about how many times you misread something, and had to re-read to gain clarification. Or even worse, how many times you've misread something, and took the entirely wrong meaning from it.
On tons of forums/message boards, and now even transcending into social media and the actual news, I see tons of situations where something was quite obviously misread (because it was a joke, trolling, serious, or simply missed a word), and it blows up into a huge issue; when the whole thing is a result of poor reading-comprehension.
[TL-DR] To summarize, I suppose: I don't mind mistakes in your average situation. In areas where language is important, though, you can't afford to make mistakes. Unfortunately, because so many people aren't in serious situations and therefore don't write carefully, even serious situations are now constantly misunderstood.