I can think of one possible escape from that fate: some serious and dedicated interbreeding between races. Lots of sex. Lots of cute babies. Everybody wins.
A couple of problems with that idea:
1.) That requires a calculated attempt to eliminate ALL existing racial groups, aka genocide.
2.) Some groups are far larger (and with higher birth rates to match) than other groups, currently. The resulting mixed single human race would be comprised of far more of some peoples' DNA than others' and those who had bred most irresponsibly would end up rewarded for that behavior. Not to mention the fact that some groups are characterized by far more dominant traits and others are characterized by more recessive traits which means that even if the planet were comprised of exactly 3 billion whites and exactly 3 billion blacks, and nobody else existed or ever had, whites would have a legitimate basis to feel that some of their defining characteristics stood to be lost under such a proposal. It's true that light colored eyes, freckles, reddish hair and such don't disappear 100% of the time after one generation of mixing, but they *tend* to not show up and they also tend to get swamped and disappear with subsequent mixing, and at best appear in a very dulled and reduced form. This problem is only made much worse by the fact that, as previously stated, the groups with more dominant traits are currently far larger and this would just make the swamping / genetic destruction angle all the more pronounced.
3.) Many people (from all groups) exist now, and could be assumed to exist in the future, who would not want to take part and who wish to preserve their group. What would we do, force them to pair off with someone of a different race? How far would we be willing to go to achieve this dreamed of "zero diversity" world?
4.) Many people (including a LOT of nonwhites, possibly even the vast majority of them) consider fully white babies/adults to be much cuter / more desirable than mixed babies. Especially when the mix is with blacks. In the nonwhite world, light skin is prized. Light hair and eye colors are prized and seen as desirable. Among East Asians, Amerindians, Middle Easterners, etc. blacks and their associated genetic traits / appearance are seen as undesirable, generally. Even within blacks themselves, these attitudes are quite common. Light skin seen as preferable to darker skin, "good hair", skin lightening creams in Africa, etc.
5.) Many of us feel we have good reason to suspect the resulting mixed humanity would be less capable of facing the challenges of the future and of technological civilization than current existing varieties of humanity are equipped to do (Whites, Jews, East Asians)
Of course, the biggest issue is that this idea is just completely pie in the sky and unworkable but I know you're not proposing it in an entirely serious manner. We've both obviously heard many other people suggest it before, so I'm just using this as an opportunity to point out some issues with it.