Nothing substantial.
They can participate in any of the district extracurricular activities that any child attending public school can. (per federal law)
What do home school children miss out on in life that regular school children have?
Crappy cafeteria lunches.
Each case is different. Much would depend on the quality of the instruction.
We could wonder if some social skills might be not be learned, especially if the child is always schooled at home, alone.
Less interaction with Children of their own age group which could drastically limit their Circle of Friends, which could lead to poor social skills.
I am a home school mom. My first born, I never was able to home school her. She graduated from public school. There was bomb threats, peer pressure, horrible school officials and a rapist. These were just the high lights because fights and campus police was just the every day norm. 😠I WISH she could have missed out on all that distracting crap! My second did public school elementary, home schooled since her first year in Jr. High. She is graduating next year. The youngest in her classes. She missed out on mixed locker rooms where boys and girls dress out together according to the "gender they associate with that day." As well as gender neutral bathrooms where the schools will not tell you but sexual assaults happen more often then you think. Oh yah and in Cali you get suspended if you use the wrong pronoun to address someone who appears to be a certain gender. My daughter however volunteers year round with pre school aged kids at one church and leads a group each week with her peers from our church. Plus she is always invited to the other home school outings which if I have a car I do take her. (Carnivals, amusement parks, water parks, trampoline parks, regular parks, restaurants,). My third started out in public school. She was bullied and put up with it for many years. Her teachers said she was behind in math and her grades were not doing well. When I witnessed a bully put his hands on my child, I reported it and the school did nothing but PROTECT the bully. I yanked her out and she's been home schooled for the last 2 years. Home schooling taught her just how smart she really is. She is doing work above her grade level and she is much happier. Home schooling boosted her self esteem and her academics. My youngest child, he will never see a public school. I begin home schooling him a week from tomorrow. 😊 And he is the life of the party when he is in his social environment. I get compliments on how happy, behaved and fun he is to be around by people all the time. For the Yin and Yang household, home schooling works well.
Honestly, it depends on the parent. I have known quite a few families that home schooled. Almost all attended home school field trips, and had the children enrolled in some kind of program(s) so their children still interacted with other child in their age group. Things like scouting, gymnastics, martial arts, or church groups.
I knew one family where the mother mother tried to control everything in her children's life. She put them in girl scouts, but pulled them out after a couple of months because another little girl was rude to her daughter, and didn't think the troop leader did enough to correct the rude girl. She knew how it went down, because she attended the meetings with her daughter. This is how not to do it and even meeting the family again after the oldest was in college the mother was still controlling her daughter's. The oldest was in college and still living at home. She could have gone to a college two hours away, that had a better program, but her mother wouldn't let her. The younger daughter was looking at the other college though, and you can tell her mother wasn't happy about it and said they would discuss it more later. I don't know where she went, but I hope she got out.