T's office is a no-shoe zone, which is pretty normal here for indoor workplaces. It wouldn't be weird if shoes were allowed, but I would say that it is more common to have a shoes-off policy, especially for health care related workplaces. He wears sandals, I wear socks. (Well, he's got socks on as well - bare feet are not considered okay at work.)
Different countries, different customs. I know that stockinged feet are considered slightly rude in many cultures, but in countries where you have to wear warm heavy/waterproof boots for several months every year, it makes sense to remove those shoes at work, so you don't have to walk around in them all day. (I wear sandals at work, too.)

As an aside, I often perch on a desk while teaching, and my students frequently do so, too. It had never occurred to me that anybody could find that revolting.... I have to check with the locals to see whether I should stop doing that! For me, it's not even slightly gross, and I certainly have no problem sitting where people have had their feet, as long as they were not wearing shoes (that would be gross.)