You only have to look at how the snow last winter affected food supplies to see that supermarket shelves can quickly run empty when supply chains are disrupted. I lived in a large city, but supplies coming in were disrupted and I had to walk around several shops to be able to do a "proper" food shop that weekend. In October, I'll be living in a rural town with less food shopping options options- I'll definitely be building up a buffer for no deal if that still looks likely when I move in.
If we no-deal, there will be disruption to transport across the channel, which is how we get a lot of food into the UK. We only produce about 50% of our own food, and then another 30% comes from Europe. A lot of what comes from RotW also comes through European ports.
I remember reading in February that only 17% of the usual traffic would get through at ports each day in the event of a no deal. The government have explicitly said they will prioritise medicine and chemicals needed for water treatment- so say 10% of our usual food imports get through. I would imagine there won't be evenly distributed around the country, either.
So people are:
-Getting in a supply of essentials to get them over the initial bumpy first few days/weeks.
-Getting in a store of European favourites that may increase in price or be hard to get if we exit the EU without a deal.
-Getting in a longer term store of food as a buffer against price rises and potential civil unrest.
Don't forget that some people rely on "free-from" food due to allergies and intolerances, and some children with SN are very particular about the food they will eat.
Building up a store cupboard slowly over time doesn't do any harm, and will help mitigate the impact of any short or mid-term shortages.
As I'm moving, it's going to be tricky for me to build up any major store, but when I do move I'm going to try to make sure I have a supply of food to keep me going (I'll be living alone, so I think this is a sensible thing to do anyway) if there are problems with food supply.
If you think there are going to be problems with medicines getting through, why don't you think there will be problems with food coming through?