Learn Hardcore Japanese: kutu ga doro de kitanai node, genkan no soto de nugimasita. - Because my shoes were dirty with mud, I took them off outside the entrance.

Breakdown of kutsu ga doro de kitanai node, genkan no soto de nugimashita.

Why is 靴 marked with が here, not は or を?

In 靴が泥で汚い, 靴 is the subject of the description dirty with mud, so が is natural.

が = marks what has the property
は = would make shoes the topic, as in As for the shoes, they're dirty with mud
を would mark the object of 脱ぐ in the second clause, not the subject of 汚い

So in the first clause, 靴が is correct.

What does 泥で mean? Is this the usual location marker で?

Here, で is not marking the place where something happens. It shows the thing causing or making the state: dirty with mud.

So 泥で汚い means something like:

This use of で also appears in sentences like:

Why is it 汚いので and not 汚いですので?

In Japanese, subordinate clauses often use the plain form even when the main sentence is polite.

So this pattern is very common:

汚いですので is possible in some formal situations, but it sounds stiffer and is much less common in everyday speech.