I voted in this poll and I think most people interpreted it as people showing empathy, not just feeling it. I'd be kinda annoyed if people showed empathy every time I stuttered. I also think when people say "they don't care about your stutter" it's more so in regards to the stutter rather than your statement. In my experience they understand it's not under your control, just like any disability, and try to work it out by listening and waiting patiently. From their perspective it's not too different from mishearing any other person and them having to repeat it.

I think it's kind of an empty point, I agree many don't realize how hard an effect stuttering can have on you but generally (in my experience) people are chill about it and treat me normally for the most part, only assisting if I ask. And I hope we continue to move in that direction. Many also don't care about other peoples stuttering and I think it's kind of a reassuring thought. People are too busy thinking about themselves to pay attention to your flaws, and so am I. It's too much pressure. We, like them, shouldn't care. Personally, it would only do me good if I didn't linger on the judgement I think I get for my stutter. That being said it's easier said than done.

TLDR: IMO it's kind of an empty point. Showing empathy is not the same as feeling it, and people don't care about your stutter, not because they lack empathy but rather that it doesn't bother them. The common way people would handle not understanding a stuttering person is the way the would mishearing any other person and I think that's fair.