Permit me to ask you a question.
What if the amendment in question had been the First, and not the Second? Would your opinion on showing ID be the same?
In other words, five men are in Culvers (great restaurant, btw) discussing politics. Someone sitting near them overhears the conversation and calls 911 because they dislike the conversation. The police arrive while the conversation is still ongoing, and determine that it is simply protected political speech. Would you still feel that the police should have demanded to see ID, or should they simply recognize that no crime was taking place, or about to take place, and been on their way?
This discussion became moot with the release of the 911 recordings.