Re: your reblog about ladies' etiquette/conduct manuals, one thing that surprised me was that those manuals (e.g. The Mirror of Graces (1811)) encouraged exercise for ladies, especially in the form of long walks! that re-contextualized Pride and Prejudice to me; I used to think Caroline (and her sister) calling Elizabeth "blowsy" for walking and getting her hem muddy was her being stuffy, uptight, a stickler for rules, etc. while Elizabeth was being the cool heroine who was mildly improper in a cool way or something. But then I realized, actually Elizabeth was the proper one with correct manners like a "good lady" while Caroline was being improper and even crude/vulgar for her time, especially for slandering another lady's good name! I feel like sometimes popular culture frames Elizabeth as a more Jo March-like heroine who rejects traditional social norms when actually she's really concerned with propriety and social/moral laws - in fact, that respect for propriety is one of the things that impresses Darcy, right?
(one could argue that there are instances of the inverse too, e.g., Caroline's "warning" to Elizabeth about Wickham is basically "he's a mere steward's son, what else can you expect from such low class people" which Elizabeth disregards, but in the end Caroline was right about him... but there are kindhearted servants too, like Mrs Reynolds, so surely that disproves Caroline's assertion?)
So no, I don't think so... if we look at all the context in the novel, it's pretty clear that Elizabeth was the one doing something improper or at least somewhat risky. From the quotes surrounding her walk, it seems the problem is 1. the distance walked solo and 2. the fact that it was muddy (dirty). The Bingley sisters are being mean/trying to exaggerate Elizabeth's faults, but Darcy agrees that he'd never let Georgiana do something like that. So all in all, this was not within proper conduct:
Elizabeth, feeling really anxious, determined to go to her, though the carriage was not to be had: and as she was no horsewoman, walking was her only alternative. She declared her resolution.
“How can you be so silly,” cried her mother, “as to think of such a thing, in all this dirt! You will not be fit to be seen when you get there.”
“I shall be very fit to see Jane—which is all I want.”
“Is this a hint to me, Lizzy,” said her father, “to send for the horses?”
She was shown into the breakfast parlour, where all but Jane were assembled, and where her appearance created a great deal of surprise. That she should have walked three miles so early in the day in such dirty weather, and by herself, was almost incredible to Mrs. Hurst and Miss Bingley
“She has nothing, in short, to recommend her, but being an excellent walker. I shall never forget her appearance this morning. She really looked almost wild.”
“She did indeed, Louisa. I could hardly keep my countenance. Very nonsensical to come at all! Why must she be scampering about the country, because her sister had a cold? Her hair so untidy, so blowzy”
“Yes, and her petticoat; I hope you saw her petticoat, six inches deep in mud, I am absolutely certain, and the gown which had been let down to hide it not doing its office.”...
“You observed it, Mr. Darcy, I am sure,” said Miss Bingley; “and I am inclined to think that you would not wish to see your sister make such an exhibition.”
“Certainly not.”
“To walk three miles, or four miles, or five miles, or whatever it is, above her ancles in dirt, and alone, quite alone! what could she mean by it? It seems to me to show an abominable sort of conceited independence, a most country-town indifference to decorum.”
Walking is fine, walking 3 miles and being covered in mud when calling on a neighbour, not fine. This is the only time Elizabeth's walking is commented on, otherwise her walks seem to be within the limits of propriety.