This was probably the smartest suggestion thus far.
I doubt anybody is actually allergic to tannins, because there are so many other products than wine that have tannins. However, most of the suggestions above tend to have quite a bit of tannins, even though you don’t taste them.
The only red wines actually low in tannins are Barbera, Poulsard and the other few varieties that are actually very low in tannins. Pinot Noir and Gamay might be low in tannins compared to Cab, but you can still make some impressively tannic wines out of them if you macerate long and aggressively. You can’t make Barbera or Poulsard tannic no matter what you do (unless introducing some wood tannins to the wine during the aging).
Of course the other option is to go with the cheapest mass-marketed red wines. Most of them have their tannins filtered away for that smooth, soft and juicy mouthfeel the consumers love.
But barbera is VERY high acid, which I’ll lay bets the guy won’t like. Barbera is the antithesis of cheap cab.
Ideally it is, sure. However there are producers who consider it a good idea to make 15%+ ABV, super concentrated barberas that are the complete opposite to the beautifully savory and highly acidic G. Rinaldi Barbera and as such would be a good expensive option for someone like the person the OP is describing.
Even ripe, oaked barbera has a fair deal of acid. I just can’t imagine that’s the next step for this guy in exploring wine.