I homeschooled my Twice Exceptional sons. They are both socially awkward and probably qualify for a diagnosis on the Autism Spectrum, though they don't have a formal diagnosis.
They did much better socially and were much happier with being removed from an environment that was very stressful for them. However, if you met them now and only knew that they were homeschooled and are obviously socially awkward, you could easily leap to the conclusion that they are socially awkward because they were homeschooled.
Additionally, there is a cultural element to any social outcome. There is a certain amount of being inculcated with the right behaviors for the setting. Being homeschooled means you lack some of the same context as the majority of people who attended school. So it's easy to read as socially awkward because you don't readily fit in, even if your social skills are actually better in some important ways.
Think of how immigrants tend to seem awkward and don't readily fit it. It has nothing to do with whether or not they have good social skills. They are just strangers in a strange land.
The social aspects of school aren't always positive. Most adults that have difficulty interacting with other people tend to have had a bad time in school. I've seen a little bit of naivety from home schooled people but I've never seen someone full of hurt like I have from people from public school.
A lot of parents choose to homeschool specifically because they don't want their child pidgeonholed and pipelined into special needs classrooms.
If it works for them, great, not hating - but I doubt that's what people in this thread mean when they talk about homeschooled kids having a normal, social life.