I think human behavior leans towards hoarding, especially in times of scarcity. Once the shelves empty, I won't be surprised to see grocery store shelves empty as well, as folks can't quite discern between availability of food and availability of other consumer goods. I think some of that fear may be justified - packaging relies on some imports whether it is parts for machines or just general packaging.
I've stocked up just to avoid the rush. Yes, I've stocked up on food. My weekly spend at the grocery in May (for example) could be avoided completely if necessary, but it's also set up to just buy fruit, veg and dairy. If those become unavailable, I have options.
I've also stocked up on some more random items, like filters for my furnace's air purifier and fridge filters. I suspect those are made in China and even if not, it is likely that some of the material is. Some of those are expensive enough that I'm okay with stocking up a couple of years of those. My furnace filter, for example, is over $100 each, but that saves me money by buying it myself as the HVAC company charges another 50%. The issue is that it comes in a box of 2, so I have to shell out $200 to get a filter. I'm sitting on 3 years worth now. They'll get used though, and they don't go bad. Worst case, I have less storage room. Best case, I ride out the price increase for a couple of years.
I've also stocked up on commonly used personal care products - like dh's razor blades, extra toothbrushes, our fav shampoo/conditioner. Those all have plastic in them, and I'm a bit wary of anything with packaging (which I admit - is a LOT of stuff) and just want to make sure I beefed up my supply of those.