I am not saying you did anything wrong OP, or that you actually did mean anything, and for the record, I would have found it annoying too (the sax playing,) but I do think the neighbour may have been a bit offended by your words. Maybe he shouldn't have been, as you meant nothing by it, but he clearly was annoyed according to the reaction your explained in your first post
You said ...
Neighbour looked shocked, mumbled something about playing in a different room... like, as though he hadn't realised we could hear it. It's a fricking saxophone, of course we could hear it. Anyway I said nothing. We walked on in silence.
I relayed the conversation to DH when we got home and he made this face 😬 But then laughed and said not to worry about it. But then yesterday the guy's wife blanked me in the street.
So the neighbour mumbled under his breath and seemed shocked and said he will get the kid to play in another room, and then the wife blanked you in the street. A MONTH LATER... I am willing to bet that she didn't accidentally blank you either.
They are clearly still pissed off. Some people do hold grudges, especially if they think someone has been rude, and hasn't tried to make amends. And maybe they think you are pissed off with them.
Did you actually speak to the wife? Or just smile? Half smile? Nod? What? You weren't very clear.
This obviously bothers you, (or you would not have posted here!) and it is seemingly bothering them, so you need to talk to them. Knock on their door and ask them if everything is ok as you are worried you offended them by mentioning their son's sax playing. Do you really want bad feeling with your neighbours indefinitely? I know I wouldn't.
Again, I don't think you were rude, or you have done anything wrong but you need to deal with it, as it's clearly bothering you, and is possibly bothering them too by the sound of things.
And I think it's rude for people to call them insensitive arseholes and 'professionally offended' and so on. People are entitled to feel slighted if they think someone is having a pop at them. And as I said, I think many people would have reacted as they did, because imo, the OP's words did seem quite passive aggressive; even if she didn't mean it to come across that way.
Have you heard the sax since you mentioned it a month ago by the way?