IMHO, a public shelter is the last place I would want to go in an emergency. If you come properly equipped, then it is likely you will not be admitted in an emergency without at least identifying all your provisions to whoever is in charge, and run the risk of them being confiscated sooner or later in a "Triage" environment, where you either give up the goods or get kicked out, maybe without them anyways. This may not be the program at the shelters now, but it is a plausible enough probability that I would not take the risk. I've seen firsthand how it works elsewhere. What are the advantages of a public shelter over a private one?

Well, maybe you will have better access to certain services, provided there is a doctor or two and some nurses that are in the shelter with you, and they have the supplies they need to do their work. Likely there will also be a greater exposure to communicable disease, and there's no way of knowing the condition of the supplies you would be relying on. Then there's the security issue, do you really think they will let you bring a firearm into the shelter with you?

I would rather find a suitable location myself and make my own shelter and equip it as I see fit. Then if TSHTF, I am not relying on whether or not someone else knew what they were doing and could take care of business.