I still wear a light jacket inside often as I keep the place between 60-65. Stopped wearing shoes inside as I hate cleaning. That's how I was raised though, and wearing shoes inside isn't terribly uncommon here. Maybe it's a regional thing, maybe a class thing, but people asking you to take off your shoes when you visit is way less common than not. I have to ask people to take off their shoes when they come over and it's considered bougie.

I usually don't get mud on my jacket when it rains, how do you even do that?Unless it's a complete downpour, microburst levels of water, the jacket would only be slightly damp. Jackets don't hold water by design, and if it's drenched I'd put on something else. If your shoes are muddy, wet, or covered in snow then you take them off.

Of course, I put it on after I take off my shower coat