Let's go over the possibilities here:
1) You can't bring pets or shoes, but a shirt is required.
2) You can't bring shoes for your pet, but a shirt is required.
3) You can't bring shoes for your pet, but a shirt for your pet is required.
4) You can't bring pets, and you must wear and shirt and shoes.
5) None of them are required.
6) You can bring some Tylenol because your head hurts after reading this stupid sign.