He's only one year old so he won't understand things like being taken home from a playdate. At that age you just have to helicopter a bit (not a bad thing in this context) and look for signs he's about to do something naughty and prevent him or stop him in the act.
If he does take food etc then give it back to the child and explain "That's Andy's" (or "Not yours") then take another piece of food (if it's offered) or your own snacks you've brought and place it in front of your child "This is yours". You don't need to sound angry, IME. Just explain in a clear and matter of fact way and feel confident about it.
Agree Janet Lansbury's approach is really good. Firm but respectful of the child, never fear-based and age appropriate. The website is better than her book IMO.
He will not understand big long explanations, 2-3 words is about the max, so try to keep your explanations this simple, and he won't understand being punished. The way to teach him boundaries is (tedious) but just to prevent/stop the behaviour in its tracks every time, redirect to or model the behaviour you want, and remind every time, don't expect him to remember to do things the right way yet, especially if it's a new context (e.g. new place, different food, different friend).
Children of this age can't really follow directions against their impulses, so it is not that he is ignoring you as such, it's just that expecting him to follow a direction in this kind of situation is not age appropariate regardless of whether he understands. You explain/direct (e.g. "That's not yours" AND combine with an action (taking the item away, blocking it from his reach or moving him back out of reach of the item) - telling him and expecting him to comply of his own accord comes later, and slowly, first for easier (less high-value) things and only later for something he REALLY REALLY wants. Children vary in the age they can do this, but almost none of them can do it at 19 months old.
At this age they don't understand sharing or property, so it is normal for parents to share food between toddlers just to avoid a huge scene (I would make sure you always take more than you need yourself, so it can be shared back reciprocally) BUT you can still stop him from taking it out of a child's hand/plate or hold him back and model/show that you say please nicely before randomly taking out of somebody else's pot. If he can't say please, that's not at all unusual and is perfectly OK but you can say please for him.
Some children are more persistent or more biddable than others! It's likely nothing you've done but maybe it would help to be a bit firmer when addressing it :)