Christianity is about only one thing in the end: reality, the whole undiluted truth about God and Man. The Church has expended 2,000 years fighting the least departure from truth - departures which look like mere trifles to outsiders - as though all eternity depended upon the outcome.
Race and "human bio-diversity", rightly understood and prioritized, capture one aspect of the reality of creation. Theologically, race is a consequence of the Fall, the separation of tongues at Babel. That doesn't make it any less real, nor does it mean that race is not somehow incorporated into the divine will. There exist groups of men who share common ancestors, who also tend to share certain physical and psychological and intellectual traits, and it is fitting that such groups be recognized in human language. Race does exist, and race does matter.
However, unlike sex, race is not a system of fixed categories. It is something that changes with the conception of every human being. Over the centuries new races emerge and old races are transformed. Race can be likened to a large, historical extended family. Families don't just keep to themselves, but they make alliances, they intermarry, they adopt, they wander and mingle and conquer and steal, and they learn from other families.
The Church has always acknowledged and accommodated particular racial and cultural differences, while at the same time minimizing the potential for conflict and emphasizing their common humanity. Racial integration is neither required nor forbidden; interracial marriage is neither encouraged nor discouraged. What is required is charity, justice, prudence and sobriety. It is true that, in recent times, many of the Church's prelates seem to have lost their doctrinal moorings on this topic, but the Church doesn't bind anyone to the transient political opinions of liberal bishops or even popes.
I am pleased to have found that Matthew Anger's article on "Race and the Church", from 2003, is still online at the now defunct Seattle Catholic website. The entire piece is worth reading, but I select the following quote for your consideration:
Modern policies, whether "racist" or "anti-racist," have their roots in the same mindset—the idea that human relations must be forced to fit a procrustean ideological model. Sadly, the denial of the supernatural results in a denial of even the most blatant natural facts about relations between the races. What has the Catholic response been? Unfortunately, the spiritual hiatus of Vatican II short-circuited what might have been a sensible as well as peaceful resolution to modern race issues. While Catholic ethicists prior to the Council were balanced and restrained, by the 1960s, many in the Church unthinkingly aligned themselves with all aspects of the "anti-racist" or "desegregation" movement, not only positive elements but highly dubious ones as well. By contrast, the traditional axiom that should still be invoked today is that the Church favors neither forced segregation nor forced integration.
The instinctive tendency for most individuals is to associate with others of the same racial background. We should not artificially force intermixing in such a way that fosters social strife and, in the process, destroys beneficial social supports that people have built up over generations. This is the case with desegregation in this country where blacks have undoubtedly gained in some areas, yet many have bemoaned the loss of a tight-knit and supportive community life that existed even in the worst days of slavery. Clearly the hypersensitivity about racial differences, the often brutal enforcement of "multiculturalism" and the fear that a racial slur lurks behind the most casual remark, has no part in Catholic thinking. Nevertheless, any secular theory of "racial classification" and strict separation becomes impossible when applied to daily life as, for example, in the case of people with mixed ancestry. Finally, any supposed benefits of racial segregation are belied by the ethnic tension in areas like the Balkans where the contending parties are racially indistinguishable. The deeper factors at work are, and have always been, culture and religion.
As with slavery in the classical world, the resolution of racial problems must be gradual and prudential. Though speculation as to the future of race-relations is difficult, one should keep in mind that there may also be events which would completely alter our priorities. A restoration of the Church and traditional teaching, for instance, would unite men in a cause that would quickly leave political, national and ethnic rivalry well behind us. One may certainly hope so.