The difficulty would seem to be that you cannot at the same time work in a different way of representing class divisions and expect the author's own conventional observations about such divisions to retain force. This production seems to want to have its cake and eat it, and I suspect that this is because the nature of Forster's writing: it is very difficult to abandon the whole this-is-how-people-behave-in-the-Edwardian-era because it is such a central part of his books.
Shakespeare is different because his plays incorporate a kind of timelessness: they are either set in a past which he and his audience know relatively little about/don't care about keeping historically accurate (the Roman plays, the chronicle plays) or in an imaginary world. No points are made by acute observation of one particular moment in time.
Forster very much depends on the precise observation of social mores in his own time. That is how he works, that is how he makes his points. Take that away and you lose much of the point.
Of course you should update historical drama (though possibly not Forster). But if you do, then you need to be bold enough to eschew the attempt at accurate historical representation in the first place. You need to make it more timeless, not pretend that you are doing a historically accurate costume drama. Branagh's Much Ado, with a black prince of Aragon, worked brilliantly, because his and Shakespeare's Aragon is a place outside of conventional geography or history.
Yes, there were black people in Edwardian Britain (though no doubt far more people of Indian descent than African or Afro-American). But it is highly unlikely that they could have married into even the lower middle-classes without causing comment. And the same with the black maid. It may not have been impossible. But people would have talked, done a double-take first time they met them, registered surprise. In the docks, yes no doubt. But in Leonard's case, it would be the colour of his wife as much as her class that caused a reaction and that would be talked about.
If the script writer is prepared to take that on board, then fair enough. But my suspicion is that they are not going to do that, but will just carry on pretending that this is historically accurate Edwardian England and everybody has the same reactions as we do now. Which (as a pp hinted) has the effect of completely downplaying and ignoring the struggle of black people in this country.