So writing and speaking, while having a lot of linguistic overlap, are just different beasts.
(Ironically I think my grammar in this comment is not great, but FYI English is not my first language-- I'd appreciate a correction if appropriate)
I think I pronounce all three differently (Southern RP-ish (as in not farmer) BrE) but 'their' and 'they're' are close।
Rhotic AmE though clearly distinguishes those, and I can imagine them all sounding similar in that sort of accent।
I think I understood them, but I can never be sure, because in order to understand something with improper grammar, you usually need to "fill in the gaps" with the most reasonable assumptions possible, and those don't necessarily line up with your interlocutor's beliefs or intentions.
Putting words in other people's mouths is often required to "lubricate communication along", but it should be done as minimally as possible if the goal is for people to understand each other.
See Grice's cooperative principle: https://en.wikipedia.org/wiki/Cooperative_principle
What's bullshit is people who think they know what other people think.
For example, "you're" and "your" are two very different words.
Let people obsess. They're not hurting you.
And in fact why would I have? I was replying to something someone else said in reply to you, not even related really except via parent to your GP comment.
The other thing is that writing on the open internet means that potentially many people will read the writing. Good grammar is borne out of routine, but this only works if the people practice the right thing - if they practice the wrong thing, then next time they'll potentially do the wrong thing by habit. So really, good grammar depends on reading texts with good grammar. It's also how we pick up vocabulary. Putting these things together, I think people owe it to each other, and the collective humanity, that they produce quality writings on public places.