Hi rodi. You have to be a little more specific. There are thousands of wines so if you refer to "that sharp tart taste" it's hard to know which tart taste you mean.

But I'll give it a shot. When grapes ripen, the sugar content goes up, the water content goes down, and the acidity decreases. However, if the grapes get too ripe, they'll have too much sugar for the acidity and if you can get the yeast to ferment all the sugar, your alcohol content will be off the charts and the lack of acidity will make the wine seem unbalanced and flabby. To make good wine, you need acidity and for that reason some winemakers in hot climates add a little acidity to their wine.

So if the wine does not have some tartness, it's not going to be good, at least to wine drinkers. That however, may be exactly what you yourself want. On the other hand, you can have both a tartness and also a sweetness, if that makes sense, and that's what the better sweet wines have. Think of something like sweet and sour chicken from some take-out place and that's the idea.

Also there are different kinds of acids and some have a bitterness that others do not. Some white wines for example, go through a second fermentation after the alcoholic fermentation from grape juice, and in the second one, the malic acid is changed to lactic acid, which is softer and feels "smoother" and somehow fatter in your mouth.

So for whites, you would then avoid those that don't go through malo-lactic fermentation. Some winemakers don't put their wines thru that second fermentation because they want to keep a crisp tart quality. If you try most riesling from Germany for example, or any number of white wines from Spain, you will find this quality. Some riesling in particular, can be rather sweet too, which plays against that acidity - think of fresh lemonade where you still taste lemon but also sweetness.

On the other hand, a lot of chardonnay from California often goes through malolactic fermentation and then it also goes into oak barrels, which makes them seem buttery and fat in the mouth.

As far as specific examples for red wines, at the low end there are things like Yellow Tail or Two Buck Chuck, which have basically no tannins (that make your mouth feel dry), low acidity, and a little residual sugar. Many people like those wines and if they appeal to you, then by all means enjoy them.

Try fruit wines.
Naturally don't focus fruits that are tart, a pie cherry wine is going to be tart just like pie cherries.

I've been making Balloon wine from frozen Concord Grape Juice concentrate that I purchase at the grocery store. Yes, it has that sharp quality rodi88 speaks of when I first siphon it out of it's fermenting gallon glass jug.
But many of us add some food grade glycerin to ours in order to smooth it out. It's called a "glycerin finish". Many commercial wines use this.

Look to your wine & beer making supplier as a source of "food grade glycerin". It doesn't take much to smooth it out.

I drink about 3 oz of dark red wine (the redder the better)
before bed time each night. My wine in it's raw stage is about as appealing as lighter fluid, but the glycerin takes care of that.