It really depends. Tanks can get filthy, inside and out, especially in Europe. Tank crews do their best to keep it clean; it is, as noted above, home. But it depends on how much time you have. If you are constantly on the move, it is very hard to keep clean. When it’s raining or snowing; it all comes in through the hatches, and the inside gets wet and muddy and there is nothing you can do about it.
It also depends on the people. Gunners can be the worst. Drivers, loaders, and commanders all live under their hatch and try to keep their area clean. Some gunners just don’t care. They climb in, put their muddy boot on the loaders seat on the way down, stomp the mud off their boots in the loaders area, then climb over into their warm, dry, and clean seat, which doesn’t have a hatch over it to let the rain in.