I've been to Aldi (won't need to go back til Friday now, possibly longer).
Everyone had to queue to get in, at least 6ft apart. Security guard was letting one person in as one came out (only single shoppers allowed, no children/couples etc). I had to wait quite a long time as you'd expect, which was of course fine and actually reassuring. The mood in the queue was quite sombre and low key but everyone was friendly and understanding of the measures. A couple of arses tried to skip the queue and took offence when told to get to the back of it though. Guard was letting older/disabled people to the front of the queue.
Inside the shelves were well stocked - no dried pasta or toilet roll but everything else. Scored my first tinned tomatoes in weeks. Fruit and veg fully stocked. And wine! Thank goodness 
There were only about 30 customers in what's quite a large store so it was actually all very relaxed. Everyone observing social distancing and no panic buying or anything silly. All in all v impressive.
What are the supermarkets like where you are?