But I also always kinda feel awkward correcting the speaker on someone else’s behalf, because maybe they do go by she/they or they/he, and I just don’t know.
Uh... You literally explained it yourself. This is exactly why people use they/them when they don't have more information. What's the alternative, to not speak about non-binary, trans, or gender-fluid people at all? Or to confront every person you meet and demand their pronouns?? Personally, I start with they/them, and change it depending on the person's preference.
I'm sorry it rubs you the wrong way, but in my opinion you're being oversensitive. It's not misgendering, it's neutral. Maybe it's just a linguistic limitation, but there's no other way to refer to someone without prejudging their gender identity, especially if you don't know their name. Obviously, if you know someone's preferred pronouns and choose not to use them, that's a problem and a different issue; definitely correct those people! But don't make perfect the enemy of good by shaming well-intentioned allies...