Our baby room is a no shoes room as babies crawl etc, you can take shoes for them to wear outside if they need it. If they go outside and aren't walking they'd be changed when coming back in. Same with food, we often have a top in his bag which has been changed and it's often covered in food. I do think they overdo getting them changed at our nursery as I have a 2yo who sometimes has a barely dirty top in his bag. I wouldn't be happy about a dirty carpet they're crawling round on though! Maybe look for somewhere else?
It depends where you go. Do you take a spare pair of clothes to nursery? The staff should change into fresh clothes if the clothes have stains on but getting messy is to be expected