Please be advised: I'm about to ruin a perfectly good joke by analyzing it.
The joke here is that it places judging people on the basis of spelling, etc., on a par with judging them based on their race, creed, color, or gender. It's a kind of ridiculous comparison, elevating the picayune to be on a par with the grandiose. And it's meant to be a slightly reassuring joke, because the people who are laughing at it do,
in fact, often judge people by their use or misuse of language, and while it may feel a bit schoolmarmish at times, it's a profound act of belonging to do so, as well. It makes people happy. (As various XKCD's attest)
But what are we really doing, when we judge people based on their use of language?
One thing that's useful to think about is to realize that a single language (say, English) really consists of dozens, hundreds, even thousands of dialects. "Dialect" isn't a pejorative term; it refers to the use of language among a certain group, which may be different in its lexicon, syntax, phonetics, or any number of other features from other dialects. Dialects are mutually comprehensible – that's what makes them part of the same language – but they can be quite different.
If you're reading this, you probably are fluent in at least two dialects of English without realizing it. One is Modern Standard Written English (MSWE), which is what I'm writing in now; the other is Modern Standard English (MSE), its spoken analogue. You might not have realized that these are actually kind of different, but if you ever look at a verbatim transcription of ordinary speech, even extremely educated speech, you'll see that there are significant patterns of difference: for example, phrases are shorter and have fewer subordinate clauses in MSE. (That's actually true of all spoken dialects relative to all written dialects; it's easier to hold long phrases in mind when you're reading)
Very possibly, you speak other dialects as well, often without realizing that you're code-switching between them depending on whether you're at home or elsewhere. For example, one of the most widespread American dialects is African-American Vernacular English, or AAVE for short, sometimes known as "Ebonic." It's actually one of the most linguistically interesting dialects, because it has grammatical constructs that MSE doesn't have, like a much richer verb structure including habituals ("he be working Tuesdays" == MSE "he often works on Tuesdays") and several different past tenses.
But if someone were to write a post in AAVE – especially if they wrote it to match AAVE phonetics, instead of MSWE spelling and MSE phonetics – it would be the exact sort of thing that gets judged as being "bad English." What's going on here?
"Bad English" implies that there's "Good English," and this kind of linguistic prescription has a name: a prestige dialect.
In the UK, the English of the City of London became the prestige dialect as London became the increasingly powerful political center of the country during the Elizabethan period; other dialects, no less ancient and shortly before no less respected, came to be seen as the dialects of the masses, of people who didn't have regular ties to the seat of power.
Unsurprisingly, written dialects tend to track prestige dialects closely, since writing has historically been a tool of the educated and powerful. This is sufficiently true that when we see any non-prestige dialect in written form, it looks shocking and odd at first: until very recently, especially with the advent of the Internet and mass writing
(as opposed to mass literacy), we almost never saw it.
When we talk about how speaking "proper English" will get you further in life, what we mean is that by being able to speak and write in the prestige dialect, you can identify yourself as being part of that social group which can do that – that is, a group which regularly hears and speaks it, and regularly interacts with the powerful whose speech defines it. (Prestige speech is, almost by definition, the speech of the powerful)
Another way to say it – one that's more shocking to American ears – is that speaking or writing in a prestige dialect is a performance of class. It's a way of demonstrating that you have membership in this grouping.
If someone can do this but doesn't, they're marked as acting "beneath themselves," failing to live up to a class standard. If someone can't do it at all, they're "uneducated" – which is to say, they haven't had the day-to-day opportunity and need to speak in the prestige dialect.
So to go back to the original joke, this is meant to be funny because judging people on the basis of "spelling, grammar, punctuation, and sentence structure" appears at first to be ludicrously harmless, a powerless method of judging people with friendly ribbing underneath. But if we pry it open a bit, what we're really talking about is judging people on their ability to perform membership in a social class. When it's aimed at people who are unambiguously within that social class, it may indeed have that nature of harmless ribbing; but when it isn't, when people say things like "you must be at least this smart to use the Internet," what it really is is saying "you must be part of this social class to belong here."
It's actually more sinister than it sounds.
If you'd like to read more about some of these subjects, some good places to start are:https://en.wikipedia.org/wiki/Prestige_(sociolinguistics)https://en.wikipedia.org/wiki/African_American_Vernacular_English
(I'll avoid giving a h/t for the image unless the earlier poster asks me to, since I'm quite certain that this poster had nothing nearly this sinister in mind, and that it was almost certainly aimed at people for whom this would not constitute "punching down." My apologies for turning an innocent post into a linguisto-political analysis.)