If you need good public transport you’re best to look at Honley or Brockholes, and Marsden or Slaithwaite to live close to a train station into Huddersfield. Buses for those areas aren’t as good, but tolerable (20/30 mins by bus vs 10 mins by train into Huddersfield)
Both areas aren’t too bad for motorways, M62 or M1. You might be prone to being snowed in if there’s particularly bad snow, so be mindful of that.
Meltham is a good choice because it’s between both areas. It can be a bit soul-less compared to Slaithwaite and Holmfirth, but probably a bit cheaper and easier to find something within your budget.
I’d not bother with Shipley or Saltaire, it’s a trek to Huddersfield in the car if that will be where your husband will be working.
Politically, there’s a wide variety of views and I think there is some tension between ‘locals’ (those who have grown up in the area) and those who have moved in recent years to benefit from the good transport links in rural locations and subsequently gentrified the areas.
Saying that, there’s a huge amount of community spirit in the area. There’s lots of local events and quirky traditions that people get behind and support. Most people will smile and say good morning in the street.
Diversity wise - most of the areas you’ve mentioned a predominantly white, but there are huge Pakistani and Caribbean communities in Huddersfield as well.