You won't need to show a vaccine card to cross state lines, only to go out to eat.

Of course its okay to walk around without an ID, no one suggests otherwise. But if you go to a restaurant without an ID, and get carded you can't order your drink.

Is the restaurant obligated to serve you then? Absolutely not.

You can enter the state without a vaccine card, you just won't be able to enjoy eating out in all the incredible restaurants in the state.