I was genuinely worried about the social aspect of HE (we took the DCs out of school age 5 and 7 due to bullying and severe stress) and I never resent being asked about it, as it's got to be pretty much the most common question. I have ASD myself and I always struggled to make friends. DD loves to play with other children, but being in a massive noisy school was making her ill, so I worried about finding the balance between socialising and sensory overwhelm.
But honestly here (with a huge and busy HE community) their social life is far, FAR better than when they were in school. They see lots of different children of all ages and from a much wider range of places and backgrounds, as well as still seeing school children at Brownies, St John Ambulance and playing out in the street etc. As well as seeing friends at various classes (HE specific gym/trampolining, writing class, trips and workshops etc) there are heaps of social meet ups at nature parks/adventure playgrounds and that sort of thing, and of course we have more time to just have regular playdates and sleepovers (something that for my DCs was just not possible after a long stressful week at school, even on weekends - meltdowns aplenty). We now tend to see HE friends during the school week, and save the non-school hours for their friends that do go to school.
They have many more proper conversations with the adults they see - other parents, club leaders, dance/sports teachers, strangers on the bus/train (I don't drive so we're on public transport a lot), museum staff, parents of my music students etc - than they did when they were at school. Their confidence has grown massively - so much that DS was discharged from speech therapy - which he'd been in for over 3 years - less than 4 months after leaving school, as he suddenly improved so much. It's been wonderful to see my shy, one-word-answer DCs blossom into confident kids who will happily chat at length about what they're learning, tell people about HE, discuss current affairs etc. I'm not saying school children can't do that - I am just saying that my own DCs did not have that natural confidence, or at least they didn't have it while in the school environment. Taking them away from that and entering a totally different, more flexible and chilled community is what fixed it for them. They get plenty of time with lots of people, but crucially they also have more opportunities to have a home day when needed, where we just relax, play and learn as a little family unit, rather than getting overwhelmed by having no choice but to sit in a class of 30 all day.
DD has also become more confident in social situations. She was, frankly, a doormat when she was at school. Again I'm not saying all school children are like this obviously! Just DD's experience. She was beaten down, literally and metaphorically. But she's found her assertiveness now, and I do think that the more varied and 'free' social life has had a huge part to play in that. Now she sticks up for herself and her friends if one of the local kids is being nasty or controlling.
However, I can totally see how it could be different if we weren't so lucky with the availability of activities and children to play with. In fact a friend who's just started HE with her youngest told me she was HEing her eldest about 10 years ago, in this same town, and she stopped after a year because there was just nothing available. But now, it's a totally different situation - we are so busy we have to turn things down, we are spoilt for choice. :)