Context is everything. The government is requiring that you give your personal information to eat at a restaurant. The government is requiring that a private place of business obtain this information and retain it in order to provide it to the government. I've never eaten out under those conditions, to my knowledge. And I won't eat at a restaurant under those conditions.
We will have a new baby some time this week or next so I don't know if I will eat out any time soon anyway. But if it were to be in Orleans, I'd use a pseudonym and pay cash.
This is quite simply going too far. I can see making a request that people participate in such a practice. But to make it into a requirement, even if unenforceable? That's just wrong.