I know this is an old post, but I just came across it in a search for something else.
My daughter is now 12 and has been diagnosed with Sensory Processing Disorder. She sounds very much like your daughter (right down to the GT program). When she was younger we just let her go without socks and didn't push it. She also wouldn't wear underwear, but that does become a problem when she is a teenager and needs to have on underwear once a month. When her sensory issues got worse and she wasn't able to get dressed, brush her hair or teeth, or do other things that were a result of the SPD worsening is when we really needed to do something about it. We went through Occupational Therapy with her and she has improved dramatically. She still hates socks and never wears them, but most of the other problems have subsided.
I'm telling you this to say, you might want to talk to a pediatrician about the possibility of SPD. He/she may recommend a good OT who can do an evaluation to see if your daughter is a candidate for therapy. She may not need it now, but may eventually, and it's better to catch it early and start treating than to have to play catch up after many coping mechanisms have become deep rooted habits.
I think its completely fine for your daughter to wear shoes without socks. I used to have to struggle and fuss with my daughter every morning about not wearing socks and underwear until it finally was too much too take and I just figured it wasnt worth fighting over. Now my daughter is 9 years old and she practically never wears socks or underwear and thankfully there havent been any issues since. The dress shoes she has to wear to school sometimes give her blisters, but she has become quiet adept at putting bandaids on her feet all by herself. It suppose it could be a sensory issue, because my daughter also loves rubbing lotion on her feet, although she still doesnt wear socks and instead just puts her bare feet back inside her shoes. I figure if shes fine with it, its not worth a battle.
Though I only do it occasionally, my son likes it if I put body lotion on his feet before putting socks on them, especially if he has been running around barefoot for a while and his skin on his feet is really dry. After a while, cotton socks get to feeling less soft, and sort of rough or stiff, right out of the clean clothes pile, and pulling them onto dry, bare feet isn't that appealing. He doesn't go so far as to refuse them, but he does like it if I think of putting on the lotion. I wonder if your daughter has a dislike of the dry-skin feeling. When I was little, I loved hand cream for that reason; I hated the feeling of dry skin on my hands.
Sounds like she has sensory issues, and I think you have a great attitude of just letting her not wear socks. It's amazing the number of parents who will get in a battle every single morning with children about something like socks.