This is a great question. Indeed, it is the question that motivated me to create my current Kickstarter product, "Ancestry and Culture: An Alternative to Race in 5e." (Apologies for the shameless self-promotion, but it actually seemed relevant here...)
The biological essentialism that underlies a lot of racism in the real world can be found in lots of D&D uses of race. I think one of the major ways in which this kind of racism shows up in D&D is by ascribing alignment to a sentient, playable race's biology rather than their learned and chosen behaviors. So we tried to address this with new character creation rules that tone down the biological essentialism.
The idea, in brief, is this:
We took the classic D&D races and divided their traits into those that are biologically heritable (like Darkvision, Size, Age, Draconic Ancestry, Fey Ancestry) and those that are communicated as systems of ideas, beliefs, etc through culture and education (like weapon training, languages, alignment, tool proficiencies, etc).
This allows you to make a character who has human ancestry but is raised by elves and so is culturally elven (like Aragorn). The zine also includes rules for making characters of multiple ancestries. So, rather than just have half-elves and half-orcs (which are problematic in several ways), you can now also make a character of elven and orcish ancestry, or gnomish and halfling ancestry. And maybe those mixed ancestry characters grow up in an entirely different culture, so they might have elven and orcish ancestry, but be culturally dwarven. This is how it works in the real world, after all.
Anyway, I thought I'd throw it out there, since it seems actually on topic. Apologies for the crass self-promotion:
Alternate PC creation rules for 5e that replace Race with Ancestry, Culture, and Mixed Heritage, for awesome new PCs. #ZineQuest2
www.kickstarter.com
Ancestry and Culture: An Alternative to Race in 5e