Poison Ivy, Oak and Sumac all have the same active ingredient, Urushiol oil. Urushiol is an allergen, so it's an allergic reaction, not a acid burn. Which also means that lye and baking soda will NOT neutralize it (but the baking soda may absorb some of it, reducing the quantity you're exposed to.) The best way to deal with these poisonous plants is to treat them as war-fighting blister agents. I am NOT kidding you.
Because it's an allergen, the more contact you have with it, the more likely you are to develop sensitivity to it, and the more likely you will have a stronger reaction to it. Burning the plants basically aerosolizes the oils, carrying it in droplet form and adhering to soot particles. Inhalation of something you're allergic to is a good way to painfully kill yourself, or be so bad off you wish you were dead. Poison Ivy is not a contagious condition, but you can spread any remaining oil residue if you haven't cleaned it off; and that includes cleaning it off your clothes, tools, and pets.
As a young kid, I'd walk through poison ivy without any problems. But when I was 6, the neighbor's burned a field off with it. We thought it was cool to run through the smoke, until a couple hours later when I came down with a systemic reaction: hard to breath, intense itching, and redness & swelling followed by blistering hives all over my body. Did I mention intense itching? Took weeks to recover and I was highly sensitive for decades afterwards. I could catch a new rash of poison ivy just from minute amounts of oil on the surface of the water on a pond or off the cat or dog.