That's possibly true. But can you always tell who is a native speaker?
Yes, to someone who likes English, or writing and language in general, most people who write informally on the web, and to newspapers' "Letters to the editor", etc. are semi-literate. English is a difficult language to get right when writing. It's very easy to get "your, you're" and "there, their, they're" wrong. Non-native speakers who are bad at learning language probably simply don't write English, whereas native speakers have to.
Also, the standard of English teaching in the last 50 years or so has been abysmal, with concentration on critical thinking, etc. rather than actually being able to spell and punctuate. Many schools stopped teaching grammar, whereas most ESL students do learn grammar. There might also be an element of non-native writers trying harder to write correctly.
When you say that nobody seems to care about it, how can you tell? A lot of people care. There are complaints in the press here all the time about the poor English teaching standards, and how first year university students need to be taught basic literacy skills.
What's the Bosnian language like on Bosnian forums and chat sites?
Interested in Language