I'm just continually astonished at the presumptuousness of some people with no more rights than anyone else, who for some strange reason take it upon themselves to try to dictate what their neighbours can or can't do.
This is not the first time we've heard such a story on GN is it!
If there are no estate rules about washing, grass-cutting, parking, or whatever else some housing estates make rules about - I'd be very tempted to put a note through the woman's door, telling her that as you have absolutely no intention of changing your habit of hanging out your washing, you're informing her in advance - as a newcomer, so she can either get used to the idea, or find a way of dealing with it. The observation about hygiene is so ridiculous it's not even worth mentioning again... but it gives you a little insight into her mentality.
Whatever I thought about the 'habits' of my new neighbours - if I was a new resident, it wouldn't cross my mind to even mention such things, it seems so appallingly arrogant. She sounds like she might be 'trouble' in the future - so I'd want to make it clear right from the start where her territorial rights stopped!