Of course the neighbours could always find this out anyway by watching the traffic on your channel as there is never any MAC randomisation involved in talking to a known access point.
They might choose a different MAC for each network, but surely for a given network they use the same one? Many people use MACs for securing access points and a continuously changing MAC would break that.
Your neighbour would be using some sort of correlation to work out the MAC anyway, so all they'll need is that it doesn't change over time for your access point.