There are definitely people who were knew who were home-educating and living in some very challenging conditions and some are also known to social services and are definitely struggling.
Some families have had home-ed forced on them, to be fair - it was that or be excluded. Basically, they were off-rolled (which is technically illegal but doesn't stop it happening)
I know one alcoholic who home-educated while holding down a minimum wage job. They lost custody of the children and that was the end of that.
Families living on boats and in caravans are not uncommon in home-education circles. We also know people who live in gorgeous 5 or 6 bed houses with acres of land.
We know plenty of single-parent families and some wealthy two-parent families and gay singles and couples who all home-educate. There's also a number of non-binary home-educated children.
There are home-educators on benefits or earning minimum wage and people on six figures and a fair few who are carers.
Home education has quite a lot of children with complex emotional needs - probably a higher percentage than school-going children - because that's probably the reason they're home-educated. And some children (and parents) with mental health needs.
Also plenty of dyslexic children, and lots of children with autism and ADHD etc (a lot of times because schools can't meet their needs but places at specialist schools for autism are few and far between and also the funding for such places is a battle that can take years) and some with children (and parents) with physical disabilities.
I also know more than one family whose child competes at a national level. They're the exception, most seem pretty average (or even terrible) at sport, obviously.
Same goes for art, music (ranging from tone deaf to grade 8 and everything in between) and a whole load of other stuff.
We have friends who have straight As (or almost straight) As and 8s and 9s and went on to vet and med school.
Equally, we have friends who have no GCSEs or qualifications at all.
I know two families with adopted children, one of whom had been in care. The only demographic I haven't come across is children shuttling in and out of care - and that is because looked-after children are by default going to be in state education and LAC is usually the top schools admissions criteria.
With that said, my children would probably not have come across looked-after children in the cosy middle class school (or the feeder primaries) down the road either, because its the sort of school that people rent property in the area for just to get their children in, and its free-school-meals eligibility is way below the national average. So home-education hasn't really decreased the "diversity" in that sense.
I'm in no way saying that home educated children "experience diversity because we've got muslim friends" or "They experience kids from different background because sometimes horse riding is discounted" because that would be ludicrious and insulting.
When I say "diversity" I mean it in the sense that an EDI manager or an LA would and not because "poor people can afford horse-riding too".
I don't think we're particularly unusual but may be we are.
Not sure if you're aware but a small number of home-educating families are in receipt of personal budgets or are technically EOTAS.
So their activities are effectively subsidised and that might include horse-riding or some other therapeutic thing (I don't generally ask people, obviously but once I did have to supply costs& receipts for an activity I organised for a family's personal budget)
Additionally, people can prioritise their income, so what is unaffordable in mainstream school might just become affordable in home-education because they're spending less on school-related stuff.
It might be the only thing they do all term but at least one family who was significantly disadvantaged (by all the usual social services parameters) did have one of their children to home-ed horse-riding (with the help of lifts from other families). I didn't ask them how they afforded it because that would have been patronising.
You seem to have no actual idea of how diverse home-education is - and why would you, to be honest.
But for some reason you're convinced that home-education is the purview of white middle class women with well-paid husbands. I'm not denying that those sorts of home-educators do exist - they obviously do - but they're not the only demographic by any stretch.