I home-schooled my kids for a little while; wish I could have done it longer. I was definitely not isolating my kids in a bubble of any sort. As a matter of fact, my kids and I are ethnic minorities - different people have guessed different ethnicities, usually incorrectly. I didn't feel comfortable with 100% student-directed, but there was definitely much more freedom than in school. My kids got plenty of socialization outside of the home - and often inside - with plenty of other people from different belief systems/classes/ethnicities, etc. And they did extremely well, both socially and academically.

Also, the reality is that many schools are segregated by class and/or ethnicity, so students attending those schools - for better or worse - see no more diversity than they might see at home or in their communities.