When I get a manuscript or see a sign that misuses its and it's and quotes, I immediately assume that the person who created it is stupid.
I understand that this is a mistake on my part. They're not necessarily totally stupid, they're just stupid about apostrophes.
It's a moral failing on my part to conflate the two, but I bet I'm not the only one. What else are your customers judging you on?
It's not just about being a grammar stickler. The fact is, we're constantly looking for clues and telling ourselves stories based on limited information. It shouldn't matter, but it does.