Realist left and alt-right
| Frogs, clowns and swastikas|
|Rebuilding the Reich, one meme at a time|
The realist left refers to leftists who are against "cultural liberalism" or "cultural leftism"  which are euphemisms for cultural Marxism, the alt-right boogeyman. This should tip you off that "Realist Left" is in fact the alt-right in yet another Count Olaf-like disguise.
"Realist left" is something that racists/alt-right call themselves when they also believe in socialism (see also National Socialists) so they can pretend to be on the left. "Realist" is short for race realist, which is something racists call themselves so they can pretend they're not racists. Those on the "realist left" rail constantly against identity politics, which is code for anything affecting black people, brown people, queer people, women, but strangely enough not white people and especially not white men, and political correctness, which is code for not being racist in public. The realist left talks loudly about how if the Democrats would just abandon their focus on identity, they could start being relevant to the middle class and the rust belt, and they know this personally because in fact most of them voted for Trump.
The term is also used by alt-right meme specialists looking to lead leftists down the rabbit hole. For example, the Realist Left Blog starts off its manifesto with harsh words against neoliberalism, in an attempt to establish left-wing credibility and to woo socialists. But it then goes on to advocate for "modest levels of immigration", "reintroducing objective morality [and] objective truth", "pro-family" and "pro-Western values", before starting to rant about "cultural liberalism". Impressionable or naive readers may be left with the impression that these are real issues that actual leftists might oppose, and not a bunch of reactionary and alt-right buzzwords.
By the time you get to "3) We are pro-Free speech, and anti-censorship on college campuses and public debate in the name of 'Political Correctness'. We oppose Islamization and appeasing reactionary Islamist political hardliners in the name of 'diversity' and 'tolerance', and support assimilation into our cultural values", it's pretty clear that this is Nazism dolled up in leftist clothing.