Is it true that serving white wine after red can upset your stomach and make you feel unwell?
I'm not aware of nasty bodily reactions arising simply because of wine-service order, though you might want to save Uncle Jimmy's homemade merlot until the paramedics arrive. The usual progression over the course of a multiwine meal flows from light whites to heavy reds. This is because heavier flavours tend to override and erase subtlety. It's just as in a typical meal, where lighter salads or fish dishes precede rich red meats.
On a gastric level (how's that for an appetizing expression?!), I've known people who find the higher acidity of most white wines to be jarring after, say, 6 p.m. So, they make the switch from white to red during the evening when they expect to be consuming more than a glass. But that acid intolerance has nothing to do with red-wine consumption earlier in the evening.
You might be interested to know that some wine experts in fact occasionally prefer to taste reds before whites, contrary to the usual order. I've travelled through Burgundy where, in particular, a few winemakers choose to present their red pinot noirs before hauling out the chardonnay-based whites. There's a sense that, because pinot is the star of the Burgundy show, particularly in the Côte de Nuits, it should be judged first and without bias. For a red grape, pinot also is light in tannins, the astringent red-wine compounds that might otherwise interfere with white wines later in the session. These winemakers argue that chardonnays, which are pretty full in body anyway, are easily able to follow pinot in the tasting progression and will presumably provide a fresh finish to the dégustation.
White after red? It's your choice – stomach willing.