This will be a bit of an essay, apologies in advance.
I’m not offended by compliments. I find it strange that anyone would even think of commenting to a complete stranger about their hair, coat or parenting skills. If a young man told me I was “nicely presented” I’d be bemused, not offended though. I compliment my friends often, because I know their backstories. I don’t compliment random people going about their business because I don’t know theirs, and I believe it’s none of my business.
And IMO this is relevant to the OP. The story about hanging up the neighbours washing, for instance. I really find it bizarre that anybody would overthink this so much. If you are worried that you neighbour doesn’t want you touching their washing, don’t touch their washing. If you are worried some random person coming along the street will think you are a pervert, get over yourself.
What you think is a nice compliment comes with baggage. If you tell someone they’ve lost weight, did you think they were heavy before? Do you think its nice to point out changes in somebody's body? Or might you wonder why they have lost weight? Are they ill, could you pointing it out make them sad?
DH’s mother used to go ballistic if he didn’t walk between her and the traffic. What on earth are they meant to be protecting you from? Men are meant to go downstairs first, before a lady, in case she falls. Haven’t seen that lately, because it’s so blooming daft.
Hold the door open for people if you want to. But be aware that it means you think they need somebody opening doors for them. It’s not polite, it used to be when women were dainty little flowers, but it isn’t any more. Most people will just smile and say thank you. If people object to you opening doors for them, just stop doing it. Nobody will be offended by that, I’m sure. (NB – opening doors – not holding the door for the next person coming along.)
I’m afraid my initial idea hasn’t changed. The people who say they don’t know what’s acceptable any more just need to pay more attention.
Here endeth the lesson. 