It's your house. You make the rules.
The same applies to making smoking rules in restaurants. The OWNERS, NOT the government.
If they have mud or dog crap on their shoes, I would make them take off the shoes.
Your house your rules.
In my house, you take off your shoes in the hallway. If you don't know beforehand, I will just remind you when you try to walk in with shoes. Similar, you don't walk in with a jacket on. Remember, you are the guest and then you abide by their rules.
I have experienced weird norms in some houses, but it's their house, their rules.
But why not wear elastic sided work boots? We have them here. "Blundstones"
I have to watch all the guys removing their work boots to go through airport security - one thing that all the increased security did was to teach some men that socks do not have to stick to the walls before being changed:p
Greenhouse gases: Any gas that, by an accident of chemistry, happens to absorb radiation of a type that the Earth, by an accident of history, would like to lose.
The internet is like a herd of performing elephants with diarrhoea -- massive, difficult to redirect, awe-inspiring, entertaining, and a source of mind- boggling amounts of excrement when you least expect it.