Use cash.

I used to use military ID for everything I could since it was technically a federal ID, yet by law, it gives up very little information about the individual compared to what is on a driver's license, but now there is an even better ID.

The US Passport card is a legal verified ID, actually kind of tricky to get since it involves all of the steps of getting a passport, but it gives up even less of your personal information than a military ID or any of the state issued IDs, and by law, anything official has to accept it as your ID because as a federal ID, it supersedes any other ID. About the only think it will not work is certain kinds of checkpoints at airports and seaports for traveling between countries which don't border the US, but even in those circumstances, if you "lost" your regular passport but still have your passport card, the worst they can do is delay our re-entry into the US, and if were to actually lose the passport or a drivers license, then the passport card is one document that can easily get you a replacement without having to dig up your birth certificate and social security card and send them in for verification.

In either event, use cash, demand cash, make a fuss when people don't accept it or won't pay it. Only cash and coin of the realm even says "legal tender for all debts public and private". Credit cards don't and all it takes is a couple of phone calls for someone to screw that up in a hurry.