Human races exist and are part of the evolutionary process. They are becoming more different over time. (This is quite obvious when you take the long-term view: They all had a common ancestor, so at one time there were no differences between them. Now there are many differences. Hence, the logic that _the differences have increased_ is irrefutable.)
Discussion
I argue against. Lets take native Americans and irish migrants. Native Americans did not drink Alcohol before. Irish have a longer history of drinking Alcohol. Since the Europeans migrated to America the native americans also adapted drinking Alcohol. So this is an example of thousands, how cultural differences get smaller through contact.
Yes, you can do things that decrease human differences. But this is equivalent to forcing wolves and beagles to live in the same enclosure. It is unnatural and oppressive, and can only happen when men with guns enforce it. (And it really doesn't matter if the men with guns pretend they are supporting the divine right of kings or the divine right of "the majority.") When people are left to their own devices, they tend to form kinship-based (that is, race-based) societies. And that is a natural and good thing.