I just replaced a 5-year-old maintenance-free AGM battery (Varta silver dynamic 95Ah 850CCA), and the only precaution I took was to wear latex examination gloves. (The car is also only 5 years old).
On the one hand, many YouTube tutorial videos by mechanics show them changing the battery with their bare hands. The only precaution they take is to ensure the negative terminal connector is disconnected first and re-connected last, but no precautions regarding chemical issues.
On the other hand, many web sites talk about the necessity of using safety googles or face shields, nitrile gloves, and even nitrile boots and aprons. They warn about the possibility of the battery gas vent splitting out tiny drops of acid, general battery acid leakage, and the danger of terminal corrosion causing burns to clothing and to skin.
- Are the risks of chemical burns very rare when dealing with modern, intact AGM car batteries? How can I reason about the level of risk I'm taking? 
- Do I need to be worried about any corrosion dust from cleaning the battery terminals? I used a synthetic scouring pad to clean the terminals. There were no obvious corrosion flakes, but I wonder if there is harmful corrosion dust and whether I need to clean all of my tools somehow so that there is no risk to my skin when I use my tools with my bare hands in the future. 
 
    