That will depend on the acid, and on how much the acid is diluted.
There are strong acids, and there are weak acids. There are oxidizing acids, and non-oxidizing acids. In general, skin reacts to strong acids and oxidizing acids.
We handle weak acids all the time. Carbonated water is a weak acid. So is the citric acid that makes orange juice taste sour.
Some weak acids, like the acetic acid in vinegar, can attack skin if they are concentrated. In vinegar, the acetic acid is highly diluted, so we can even drink it. Some strong acids, like hydrochloric acid, don’t react much with skin if they are diluted well. Our stomachs produce hydrochloric acid, and the lining of the stomach is protected from it by a layer of mucus. Even so, the hydrochloric acid in the stomach is often less acidic than the average carbonated beverage, because it is diluted with water.
Concentrated strong acids, and diluted oxidizing acids can burn skin. The acids react with the proteins in the skin and break them down, so they can no longer act as a barrier. The acid can then continue to react with tissues, killing cells. Living tissue can only function within a narrow range of acidity, and outside of that range the cells die.
Sulfuric acid is not only a strong acid, but it reacts with the water in your skin so strongly that it will create blisters. This is not because of its acidity, but because of its dehydrating ability.
You can protect your hands from strong acids by wearing gloves made of materials the acid cannot attack. With many acids the fumes are also dangerous, so you should also make sure that you have lots of ventilation. The fumes can attack the lining of the nose, throat, and lungs, as well as the eyes. Always wear eye protection when working with acids and strong bases.