I wear that shirt out all the time when I have to run to the store or some other errand because it's so comfy. Didn't even think about there being a rule against. Even if there is.....I'll probably do it anyway...

This is alright as long as you do not do anything distasteful while wearing a company shirt. While wearing the brand you are expected to be upholding company values. I only know this because I had a friend get in a fight with someone in public while wearing a Starbucks shirt outside of work, and the manager lit him up for it saying that while he’s wearing our shirt he’s representing our company and doing something like that tarnishes our image.
( imagine it like driving a company car when you aren’t working and then cutting someone off, it just reflects bad on the brand whether or not they are on the clock)

I sometimes wear mine to school when I go straight there from work. No one’s ever said anything.