Seems to be that that kind of 'satire' is pretty much racist itself, right-wing propaganda that tries to imply that all racism is a 'joke' to be sarcastic about.
Couple points.
One is that any race can be racist. But it's a bit more complicated.
Two is that 'racism' is not a totally simple thing.
I'll try to list a few 'flavors' of these things.
One type of racism is just based on a sort of tribalism - 'hating those who are from other groups'. This seems to be to be more common in more segregated/isolated groups, but not always - it's just when 'preferring your own' has some poison of hate of others added in. Think for example of prisons which are hugely race segregated and if an inmate is friendly with another race he'll get violently attacked by his race. Extreme example, but an example.
Another type of racism is just where a group - possibly low in social status - likes a group lower than it. 'White trash' in the old South desperately wanted blacks to be lower.
This might be related to the 'untouchables' in India as well.
There's often also a convenience to this racism where the discriminated group does undesirable work for others.
Lincoln ran into this running for President, promising he was strongy opposed to any idea of 'social equality for the inferior black race'.
Then there's the broader type of racism - the type where England used to have terribly murderous colonization of people 'for their own good'. When Columbus landed in the Americas, he immediately planned how many troops would be needed to enslave all the natives and force them to mine gold for him, treating them so brutally something like all but 10,000 of a million were killed within 30 years. No doubt it's similar to Roman 'superiority' over the 'barbarians'.
Then there's the basic selfish type resenting poorer immigrants and foreigners. 'Screw them'. Classic example is 'no Irish are welcome' attitudes in the late 19th century.
And of course Mexican immigrants - especially poor illigal workers - today.
Sometimes racism is among closer divisions; there's a longtime hate between many Chinese and Japanese related to Japanese superioty attitudes and history of abuse/killing. Different flavor around Russia seem likely to fit this, perhaps Russians and Chechnyans.
It's not exactly racism but it's similar to other divides - Sunni/Shia at times, Catholic/Protestant have history, Yankee/Rebel around our civil war.
There are a lot of flavors and types and things causing and reinforcing it.
It seems to be it's a very small group that is more ignorant about racism, but this sort of 'satire' isn't making some valid point by highlighting them, but rather attacking the idea that there is racism, trying to imply that anyone who points out racism is just making it up.
One of the CPAC conferences was 'Are you tired of being told you're a racisn when you know you're not'.
As one commentator said, if you're getting told you're racist so often you want a conference like that, you might be racist.
But there's an agenda among some to attack and deny the issue of racism. People who want more for themselves, who want policies bad for others whether they're racist or just selfish, would like to minimize the 'inconvenient' issue of racism. A lot of that s nothing more than pandering to people to try to get votes, telling people who want to deny racism that they're right to not care about racism and think it's all a load of crap.
That was the Nixon and Reagan 'southern strategy' that worked well for them getting the White House - when blacks broke to Democrats after Democrats finally led the way to anti-racism laws, there were a lot of votes - especially in the South - ready to be collected by those who would 'take the side' of resentful whites, even if it was sort of hidden to not anger whites who supported the progress.
Another good example of the hate to claims of racism being itself a type of racism is Antony Scalia, recently claiming that voting rights protection was 'racial entitlement'.
That's just taking anger at 'those people' for wanting equal rights and turning it into an attack.
Racism rarely is honest enough to shot itself anymore like the KKK, and even they seem to mainly say they're not anti-black, just pro-separation, leave them alone.
It's usually wrapped in some clothing to dress it up, whether legal doctrine like Scalia is attempting or 'States' rights' or economic appeals or other disguises.
The OP's a little bit right in that there are a few who wrongly say 'you can't be racist against whites' - but plenty of racism still exists.