There is an obvious problem at the heart of this thread: ethnic diversity is typically lower in 'pretty' place with lots of green. It'll even itself out eventually but it might take a couple of centuries. In the mean time the OP needs to make her own judgement about her own family's risk appetite for encountering more white privilege in their daily lives for the sake of a more rural domestic setting. Personally I am taking my cue from the fact that OP has described York - a place few would consider to be ethnically diverse - as 'lovely'.
Meanwhile back on topic, I know Herts fairly well, hope this list helps:
Watford is pretty rough and basically indistinguishable from London.
Bushey, nearby, is a bit more green but no cheaper than London.
St Alban's ('Snalbans') is posh and liberal and beautiful and has excellent commuting, but still quite a large city and very expensive.
Wheathampstead, nearby, is posh, liberal and small but I don't think has a train option.
Welwyn Garden City is fairly diverse and very green (in a 'planned landscape' sort of way) and the trains go either into Moorgate or KX. It's not too expensive either I think. Worth a look?
Hatfield is next stop in to London from Welwyn but my impression is that it's a bit rough TBH (happy to be corrected).
Hertford (where we live) is small, family-friendly, has excellent schools, walks on the doorstep, supermarkets, parks, sports amenities, theatre with lots of kid-friendly shows, restaurants / pubs, and two train options in to London (Moorgate and Liverpool St), and the house prices are way lower than Snalbans or Stortford. There are loads and loads and loads of young mums with little kids NCT should just buy the whole town and be done with it. However the trains are both only a bit less than an hour and you've then got to get to Canary Wharf (I did that for a while and hated it). And we have no shortage of tories I'm afraid. Our local FB group is definitely middle aged and a bit fretty but I haven't noticed any racism at all on it. Our builders were openly racist in my house a few years ago and I'm still fuming about it. £550 gets you something characterful with 3 beds or something spacious but more ordinary with 4 beds. www.rightmove.co.uk/property-for-sale/property-71038866.html is no more than 8 mins walk from the station and has one of my favourite walks on its doorstep - £535k.
Much the same applies to Ware, though (of course) I prefer Hertford :-).
Stevenage - don't even go there.
Stanstead Abbots has a bit of an 'other side of the track' vibe to it; some of it's white-van territory but the bit up the hill by Great Amwell church is very posh (and no doubt tory).
Roydon might be worth looking at - it's on the fast line down to Liverpool Street from Bishop's Stortford / Cambridge. Biggish village (two pubs), don't know about schools sorry, but lots of green space and your money will go further there.
HTH