It isn't rude to ask for a recipe; it isn't rude to refuse to give a recipe. But the method in which either of these things are done can be rude.
For years, the only cakes I'd make were from Betty Crocker mixes. I have some decorating skill so that is where I chose to spend my time. I can't tell you how many times people complimented the cake and were incredulous when I'd tell them it was Betty Crocker and to just follow the directions on the box.
When my mother was dying, she and I talked recipes. In time for the first anniversary of her death, I'd pulled together all the recipes we talked about and had a cookbook printed. So those are available. I mostly use the recipes as starting off points, though, changing things according to the availability of the ingredients, substituting and swapping as necessary. I've never created my own recipes entirely from scratch, though, so I don't know how I'd feel about sharing those.
I have a cookie recipe that I got from somewhere. One of my coworkers loved them so I gave her the recipe, with extra directions on how to make them because I knew she didn't bake. I don't know what she did but they were inedible. Except to her teenaged son and garbage can gut husband.
She gave me the rest of the ingredients she bought that she wouldn't use and this Christmas, when I made a batch, I gave her some so she could show her husband what they were supposed to taste like.