Great question. I'm not answering this question...exactly. Or maybe only very indirectly. (ok, I did at the end now)
Here's an anecdote. I think the lutheran church was imported with immigrants from Northern Europe, such as German and Scandinavian immigrants. So of course, the American Lutheran church members were those immigrants and their familiies, descendents.
I did not grow up in a Lutheran church, but we did attend a variety of other churches (none of them Lutheran) as I grew up and we moved a few times. Older now, and married and having a family, we moved about 7 years ago, and looked to find a church, and since neither of us are at all thinking we should be in any certain denomination, we tried out a local church, which happened to be Lutheran (just one of many chance possibilities we could have tried out). We liked the first chruch we tried, a Lutheran one.
While it's still just reflecting the local community, largely Northern Europe descent, our church does have other groups! We have Asian, African. Maybe even we may have additional. I don't think my partial native American counts, I'm too mixed American. But the deal is that we have a mix, and I'm glad we do, because if we did not it would seem to me as if it were merely a mere ethnic tradition, and not open enough. I'd feel as if we might have rejected (before I arrived) other ethnicities, or I'd wonder if we had. Now, I know for sure we do not. Because they are members.
I consider that simply fortunate, though the church does deserve it in that we are friendly, open, and very scriptural, very aiming to be the basic Christian chruch in my view (my particular view). I know of a couple of things I'd change, but it's as good as any other church type I've seen. I still don't think of myself as "Lutheran", and I don't expect to. I'm Christian, and these fellow members I think of as Christians. And I know, as a total 100% certainty, from direct first hand experie3nce face to face and extensive conversations face to face that Christians in are many chrurches of all sorts of labels, as a full certainty, not only a theory.
Not just an idea. A real thing I've seen, like seeing a car or a tree.
When I say we are all Christians, it's not me saying or hoping for an ideal (or not only), but it's an observation about an undeniable fact. Like that the sun shines light onto the Earth. Like that.
So....therefore I think it does not really matter whether a church has a lot of variety of races at all.
But it matters crucially if they welcome the stranger. That matters.