We've been lucky not to really have any bad comments etc, except for one lady (in 2.5yrs) who declared upon meeting the DCs that they were missing out by not going to school. Other than that people have just been politely interested or "oh ok", with the occasional "wow I would never have the patience" type comment (to which I usually reply "I'm not sure I have either" :o)
We get a lot of questions like "but what about SATs", "how do they make friends" etc. But I don't object to that at all, they are reasonable things to ask and people are interested and willing to find out about something they've not encountered.
TBH, HE isn't going absolutely perfectly for us right now - but in our case it is undeniably better than school for my autistic DCs, who were bullied and struggling in school for many reasons, with no support. DD's mental health was suffering so badly that there was really no option, and I have watched her healing and growing in confidence since she left school - absolutely no question it was the right choice for her.
Both DCs are so much more enthusiastic about learning now, they read more non-fiction and are always talking about science and history in particular. I think for them it's because they have more freedom and they aren't struggling in a busy overwhelming classroom. We can take our time more which for them (especially DD who possibly has LDs) is vital. They felt stupid at school.
But most surprisingly, their social life is far, far better since they became HE. I can't deny I was worried about that aspect (as someone who struggles socially myself) when we decided to HE, which is why I never object to people asking me "but how do they socialise" :). There have been issues with one local HE child bullying others, which had a huge impact on DD, so that's definitely not unique to school. Otherwise, it has been a revelation - the DCs have numerous healthy friendships at last.
We are very lucky that there's a huge thriving HE community here and we are spoilt for choice about activities, workshops etc. They do lots of HE-specific stuff as well as regular after school clubs.
My DCs are still junior age but there are heaps of classes for GCSE study, DofE type things etc so when we get to that stage there are plenty of options to help them get the qualifications they need and want.