Language matters, because it's the way we explain the world we live in to ourselves and others.
Words like lady and gentleman have changed substantially from their original meanings (both originally referred ONLY to members of the aristocratic classes), but modern usage is a two edged sword.
For most people the words are fairly benign, a 'polite' way of speaking to people we don't know well ~ particularly in groups. Most MCs begin with "Ladies and gentlemen" for example, and its not considered particularly offensive.
However, like all language, these words come with their own cultural baggage, and "mean" things that reference backwards in time, not always pleasantly.
A word like 'naughty' has come a long way from its original meaning of 'one who lives a notoriously evil life', but it still has negative connotations.
Gentleman may no longer mean an untitled son of a member of the gentry, but it retains its connotations of good behaviour, kindness to the weak and poorly situated, having the courage of ones convictions, elegance of manner and education.
Lady is another word which brings its own history with it into modern usage, and it is clear that for many people the history is more important than the modern generic usage.
This could be assumed to be because the gentry (aristocratic) classes were held up as the model of behaviour for many centuries, a position from which they have declined sharply since the death of Queen Victoria (thankfully).
'Ladies' lived a very mannered existence which few of us could imagine today. They were raised in much the same way brood mares are, to have excellent attributes for future breeding and usefulness, which included a very strict set of appropriate behaviours.
Think, for example, of the story of the Princess and the Pea. The conclusion of the story is that a TRUE princess would be so very weak, vulnerable and used to uxury that she would feel a tiny bit of discomfort through 20 layers of mattresses. Sure, it's a kids tale, but what is it telling kids?
Similarly, the 'ladies' of the past to whom we turn for clues about how young women should sit, stand, think or behave ("lady like manners") were raised to exist in refrence to to the needs of their family, their future husbands and the manitenance of the social order.
That some few escaped and went on to do other things is beside the point of the 'image' which forms the history of the term.
There have actually been a lot of writings about philological definitions of this and other terms, and what sort of impact they have had on the way modern people see the world and themselves within the world.
It makes for interesting reading, if you enjoy that sort of thing.
In the meanwhile, it's pretty clear that feminists, and most modern women, would prefer to reference their lives to their own needs and that of the people they consider important in their lives.
Adherence to a set of rules based on someone's idea of what will attract social approval 400 years ago continues to diminish in importance for most thinking people.
Also, I doubt most people ~ regardless of political philosophy ~ actually *expect* people to behave anyway at all except with the basic good manners and everyday thoughtfulness that make living at close quarters with others agreeable.
To me, that does not include women sitting with their legs angled in a lady like manner, or men doffing their hats. Both are completely irrelevant to the lives most people lead, and they won't be coming back into fashion anytime soon, I suspect.