it's horrible and bitter so only hipsters drink it (argentinians drink it too but it's some sort of masochistic national symbol) and it's a special brand of unauthentic if you buy it canned. actually i'm just guessing i have no idea what sort of stereotype these obscure wojaks are making fun of and tbh as a society we shouldn't be making more of them.
It is (or at least was) just trendy among feeeeemales of a certain age. This is the entirety of that part of the joke: they're feeeeemales of a certain age.
They gave it to Che because he liked yerba mate and that makes it actually funny.
Its a caffeinated drink like coffee but tastes more like a very strong vegetal bitter tea. There is nothing wrong with it or different to coffee in my opinion. You get coffee snobs the same way.