To pba – Of course people may ask their Rav if they want to do so. For myself and many others, (probably after talking with someone with knowledge of hashgochas) we can make our own decisions if we want to eat in a place that is open Shabbos.
Yes, I gathered it was more of an emotional thing.
Do you think you can explain what exactly the feeling is?
(Also, I’m assuming this store is not owned by jews, because if it is, you should probably not be trying to convince people to not patronize them based on your emotional reasons.)