Can anyone recommend a low-tannin red wine that wouldn’t be sweet?
Try Pinto Noir. My favorite red. And it goes with pretty much anything.
Red wines tend to lose their tannins over time, which is one reason why aged reds are so prized. But who has time to age wine? 
The problem with sweet wines is that they don’t go so well with most foods (other than desserts). And too much of a sweet drink gets kind of old after a few glasses.
When I was younger, I always served a big slab of room-temp Stilton cheese and a dry port after Christmas dinner.
Now that people are drinking less (what is WRONG with people these days?) I just have the Stilton with the last of whatever red wine we were drinking with the main course.
Pinto Noir? Michael Bay vintage? 
tl; dr
Am I the first to suggest Ripple?
gawd, that takes me back…
That old hose was demolished decades ago.
My memories will fade soon enough, but for now: Ahhh, sweet youth!
In Australia we use Merlot to ‘cut’ wines that are a bit over-tannined. So if you find Cabernet Sauvignon a bit over-powering, try a Cab-Sav Merlot blend.
A pure Merlot can be excellent. Very smooth. A not-so-good pure merlot is a bit like wine-flavoured cordial.
The best part about drinking wine regularly is the research and experimentation. And it’s a lifetime hobby.
My fingers are dyslexic.
Stilton is a great choice too, yes.
Beaujolais. Not Nouveau. But regular Beaujolais Villages or any of them that mention the village name instead of Beaujolais (e.g., Fleurie, Moulin-a-Vent, etc…) should be fairly dry. (4.0 grams or less of residual sugar per liter or wine. Compare to, say, very popular red varietal wines like Menage a Trois with 14 grams or so.)
Even without the sugar, Cru Beaujolais still taste insanely fruity and with practically no tannin. Serve them lightly chilled and enjoy.
Georges Dubouef makes a ton of them, others like those imported by Kermit Lynch, might be a little more distinctive but a bit pricier.
Best part is that even a good one is still only going to cost 10-20 bucks.
EDIT: My views on “what you should like” mirror those of Wallaby and bump above. Basically, if you like it, don’t let anyone tell you that you don’t. It’s your mouth and tongue.
What I will generally do is try to tell you about some other things (wines, foods, combos of same) that you might also like too.
I don’t care for sweet wine or even fruity wine (and most California wine I can afford is at least a little too “fruit forward” for me) but this raises an interesting question. What is the sweetest “serious” non-fortified red? Are there any truly sweet non-fortified reds that aren’t plonk? And why do some fortified reds like port get at least a partial pass in terms of being taken seriously despite being sweet?
I like wines of many calibers, but a chilled Lambrusco or similar is nothing to be sneezed at on a warm summer evening. I also enjoy red fortified wines (not port, though) like quinquina or vermouth–plain, spiked, or fizzed–and those tend to the sweeter side.
True bum wines deserve their nasty reputation, but I have received or even purchased Riunite, Gallo/Rossi and the like and enjoyed it. 
Drink what you like (in moderation). 
I drank sangria for the first time in years last month in Barcelona. When warm summer evenings come around again, I’m going to try my hand at making it.
I assume the trick is to find a cheap rioja that’s not good enough to drink on its own, but not bad enough to make you puke.
I was curious, and tried to google up some answers. Before this, I was thinking about things like Sparkling Shiraz, but, and Oz residents may differ with me on this, but I didn’t think the genre was supposed to be taken all that “seriously”. Enjoyed yes, but not dissected and mooned over.
After googling, and coming up with this pretty-good list (it doesn’t mention Sparkling Shiraz though) I facepalmed because I’d forgotten about Recioto della Valpolicella. Great examples of it are among the world’s most sought after and expensive dessert wines. More info on the two producers I’d linked. I’d thought that Amarone della Valpolicella had a touch of RS too, but I guess it’s not more than what’s now commonplace for newer versions of dry red table wine.
Anyway, the list at the second link in my post should provide new interesting types of wines to try. A lot of them are just plain fun.
Thinking some more on your question, I can’t think of a sweet red that gets respect, that isn’t a dessert wine. Although, with the RS in many high octane Zinfandels, and things like Amarone, they have more RS than the 4.0 g/liter I mentioned is a measurement for what’s “dry” or not, and yet it goes perfectly with the wine. I think for some of the really sweet Zinfandels, the sweetness actually helps things match better for dishes like Memphis or Kansas City-style BBQ. IME, it also goes great with Texas pit BBQ, though something like a Pagani Late-Picked or another fruitbomb, can be awfully tiring to drink on many of the hot days that I find myself eating Texas BBQ.
No idea why ruby port gets a pass from the general prejudice against sweet red wines, except that properly aged Vintage port can be an absolutely amazing tasting experience: very complicated aroma, seamless mouthfeel, and a monster finish. Not that it’s all that bad before it’s been aged to maturity. It goes great with Stilton (or Cabrales) though when it’s mature, I like drinking it all by itself, on the very rare occasions I get to try something like '63 Grahams, or '77 Fonseca. Still waiting to try an example of the Nacional.
To the OP: yes, it is. Who cares?
Winter is over, but sweet red wine makes the best mulled wine.
Brachetto is a sweet, lightly sparkling red wine from Italy. Not super easy to find in the US but worth trying if you can find it.