I have no problem doing any of those things alone.
I usually shop alone or with my husband (he gives great advice). I go to religious services alone occasionally, if I want to go and my husband is sick or out of town, but we usually go together or not at all. When I've gone to shows, games, or concerts, I've always gone with a group, but I'd have no problem going alone.
As for eating alone - a few years ago, I had a job where I was on weekly travel. If I'd had any problem eating alone, I'd have been very hungry.
Sometimes I went out with my coworkers, sometimes I got take-out and brought it back to my desk or my hotel room, and sometimes I just grabbed a book and went to a restaurant by myself. I generally don't go to bars alone, though, unless I'm going to a bar in a hotel for a quiet drink.