IMO, the main danger to racial intermixing is that certain subgroups will, for cultural and social reasons, vehemently oppose it; and that these groups will be, by the intertwined definitions of economic, personal, and national success these days, in the vast minority.
Given enough time, without the reintroduction of the geological barriers which allowed ‘races’ to originate, the intermixing of cultures and individuals with differing genetic backgrounds will result in a single homogenized group of humans with a largely unified culture.
This unified culture and genetic pool will retain some local variation, just as any large population exhibits, but the subgroups who have chosen to avoid intermixing will have become greatly isolated in their genetics and social order. Isolationist attitudes in general tend to lead toward extreme xenophobia on both sides, which will most likely end in either the deification or the demonization of the isolationist groups in the eyes of the majority, and in both cases, in the eventual genocide of those groups (most likely triggered by a violent or oppressive action against the homogenized majority by the isolationist minority).
The genocide may be active (murder) or passive (lack of aid during famine), but with such a large population disparity, it would seem inevitable. To see similar situations, look at any greatly disproportionate power structure involving two distinct cultural groups and enough time.
In this case, the danger lies not in the intermixing of people from different groups, but in the opposition to that intermixing. Those who do will be cut off, and will eventually die.
Then again, maybe an illness will emerge that targets a particular gene that has become common in the vast majority of mixed humanity, and one of the isolationist groups will find themselves perfectly immune to the plague. Then ignorance and fear will win the day, and the world will be over-run by different sort of monoculture, just as susceptible to a single malady as the original homogeny were.
Or vise-versa.
As far as I’m concerned, any time you only have one way of doing things, be it in terms of culture or genetics or something else, you run the risk of a single external change bringing the whole system down in one swing - no matter who is running the machine at the time. This requires not only that diversity be preserved, but that all people be exposed to that diversity. Both elimination and compartmentalization of diversity, through mixing or through isolationism, creates monocultures. And monocultures are more susceptible to attacks at a single point of common weakness.
Variety is a back-up system.