Mate Drinkers
The term mate refers to the tree that produces the leaves, the dried leaves themselves, the gourd the beverage is prepared in, and the tea itself. To avoid confusion, I'm going to refer to the vessel as a gourd. That's literally what most of them actually are: carved calabashes.
Mate the fluid is prepared by stuffing a large bunch of leaves into the gourd, moistening them with cold water, and then shaking the gourd to cause them to settle into a sloping, soggy mass with the large pieces of leaf at the surface and the fine particles beneath, so you won't slurp up any of the "grounds".

Photo credit: Wikipedia
The bombilla, a metal straw through which the drink is sipped, is then carefully inserted and used to further shape the pile of leaves, after which hot water is added to make the actual beverage.

Photo credit: Wikipedia
The gourd is passed around from person to person, and more hot water is added from time to time as the tea is consumed. Everyone sips from the same bombilla, since to remove it would stir up the pile of leaves and ruin the drink. Jean thought this sharing practice unsanitary. Jean tends to be concerned about such things.
She was experiencing mate-drinking as a social bonding ritual, an elaborate ceremony giving a group of people something to do together as they converse. Sort of like a fondue pot, I imagine.
I observed mate-drinkers on the street, particularly in Colonia del Sacramento. (Mate is the national drink of Uruguay as well as of Argentina.) These people were drinking it the way I drink my morning coffee, as a solitary pursuit.

They held their gourds in an upright position in their hands, without setting them down. Apparently it's important to keep the sloping pile of leaves in place to prevent sludge and particles from entering the bombilla. And the bottoms of many gourds have been left in their natural, rounded shape, so they won't stand upright anyway.
The drinkers carried thermoses of hot water to refresh the mate. Their faces registered pensive, faraway expressions. They spent a great deal of time sitting, drinking their mate, staring off into the distance. I noticed a man sitting on a shady bench beside the Río de la Plata. When I passed by two hours later, he was still sitting there, sucking on his bombilla.
All kinds of claims are made by people in the health food industry about the beneficial properties of mate. It's widely available in the USA, usually in tea bags or added to health drinks. Apparently if it grows in the wild and it tastes bad, you need to be drinking it to strengthen your immune system or whatever.
I don't think the people pictured above are thinking about the health-giving properties of mate. They don't seem to be much concerned about their health at all, judging from their appearances. I suspect they're just addicted to their morning drink of choice, like the way I am.