That really depends if those attributes are an important part of the character, how well the actor can fake those (e.g. Hugh Laurie without British accent in house md), and what you want to achieve. Jesus for instance most likely had a bit darker skin, but it makes sense to make him more similar to your target audience, so people can better identify with him.
> Jesus for instance most likely had a bit darker skin, but it makes sense to make him more similar to your target audience
It's a bit more complicated than that.
In most of the paintings you'll find Jesus has a darker skin tone (and hair)
Then in 1940 Warner Sallman’s created the popular light-eyed, light-haired Christ [1], Sallman worked for advertising and marketed the picture worldwide.
