Preachers, including especially my beloved Fundies, like to zero in on one word in a verse of Scripture and build a whole sermon out of it. I have complained about that, but I am going to do it here myself. In Paul's letter to the Galatians he writes There is neither Jew nor Greek, there is neither slave nor free, there is neither male and female; for you are all one in Christ Jesus. Notice he does not say "There is both Jew and Greek," but that there is neither. We do not bring our old cultural identity into the church, we are given a new identity. No one in the NT comes in and says "Wait a minute. We have to recognise the significant Zealot population in our congregation." Or sotto voce "Have you noticed we don't have a lot of Essenes in this church?" Or Pharisee, or Nabatean. The expectation for all is that they are leaving this behind as a primary identifier. Jesus did not come so that Greeks and Romans would get along better. I believe that insofar as they take on the identity of the New Covenant they will get along better, and this is one of the signs that they are growing. But that was never the point. We are to love one another as members, one of another, in the old phrasing.
Therefore I say that the early church was not multicultural in the sense we use that new word now. It was not built of many cultures. It was multi-ethnic, which is not the same thing. People brought their own foods and manner of dress, certainly, and many homely customs. Nothing wrong with that. But the early church was not trying to be a food court. It wasn't Epcot Center. That sort of celebration of differences comes from trade. Loads of fun, really. But not very relevant spiritually.
It may seem subtle at first, yet it is important. In any era we all want the Scriptures to commend what we are already doing. That seldom works out as we hope.
The era we should fear most is our own. The tribe we should fear is the one we want to belong to. Multiculturalism has become a religion of its own. Not to everyone or even most, but a significant presence. It therefore threatens to become another god for some of us.
Update: Retriever has a comment better than my post.