I am not sure where the policy of closed borders originated, but it was certainly not in the Old Testament. Amongst the concerns for social justice that are found in the Hebrew Scriptures is the repeated call to welcome the foreigner.
But someone might point out that the foreigner was welcome to join the Hebrews only if they made certain accommodations to Jewish culture and religion. The Christian would need to be very careful in insisting on such preconditions to belonging. For, unlike the people of the Old Testament, there is no expectation in the New Testament of a 'Christian nation'. We are now foreigners in the cultures where we belong. If we say that people can only belong if they conform to the cultural norms of their nation, then how can Christians legitimately justify our existence in increasingly secular cultures?
Of course I recognise that there are legitimate aspects of a nation's culture that it may want to preserve. Of course an entirely open border policy would be economically disasterous. But we should seek to be consistent in our thinking. If the ethnic group we belong to were settlers into our nation, then what right do we have to say that other groups have no right to settle here too? To what extent is immigration to rich countries a symptom of the great injustice of global inequality? Should Christians not delight to see new people become their neighbours, so that we can practice the command to love our neighbours? Doesn't belief in sovereign God free us from the fear of living in a changing society?