The sheriff of Polk County, Florida, says that thugs will check the IDs of everyone going to hurricane shelters and arrest them if they are wanted.

This means that many will risk death by staying away from hurricane shelters where they would be arrested. Even when there is a good reason to arrest someone, which sometimes there is, it doesn't justify driving per to death.

Will people without acceptable ID be denied shelter?

Note the sheriff's evidently intentional falsehood in describing people wanted for arrest, all of them, as "sexual offenders & predators". And only a small fraction of the real sexual offenders are likely to bother anyone again.