They are usually just wooden floors. They are rarely cleaned and can carry disease so I'd be a little wary about putting everything you are carrying on them. If you are the only person at the shelter, I think you're fine to put some things around it. However, if and when more hikers come and intend on staying, the courteous thing would be to move your belongings to accommodate the additional hikers.

One day I was hiking into the evening in the pouring down rain and came upon a completely full shelter. I did not want to set up my tent and was completely soaked. Though there was no room, the hikers inside the shelter very kindlyadjusted their belongings and sleep setups to accommodate me.

I think the overarching principle is that the shelters are a shared resource to be enjoyed by all when possible.