...I think she probably did like the men who were crazy about it. :-)

I found a couple of mentions of shooting in JA's letters: "Edward and Fly went out yesterday very early in a couple of shooting jackets, and came home like a couple of bad shots, for they killed nothing at all. They are out again to-day, and are not yet returned. Delightful sport! They are just come home, Edward with his two brace, Frank with his two and a half. What amiable young men!" (from a letter written to Cassandra when JA was at Rowling, 15 September 1796). However, the presence of two exclamation marks, particularly the one after "delightful sport", perhaps indicates that JA is being ever so slightly sarcastic, or maybe not.

"I think I have just done a good deed -- extracted Charles from his wife and children upstairs, and made him get ready to go out shooting, and not keep Mr. Moore waiting any longer" (from a letter to Cassandra, Godmersham, 18 October 1813).

"As a person living in late Georgian England, Jane Austen was well aware of the importance of shooting to the gentlemen of her day. Shooting is mentioned frequently in her novels" from The Georgian Index: Shooting.

If JA had really objected to it, I wonder whether she would not have made Darcy and Bingley shoot. However, shooting was a gentleman's sport and therefore, it would seem somewhat strange if they did not shoot, especially as Darcy lives in Derbyshire, with excellent grouse moors. It is difficult to say really.