I consciously consider whether to use a credit card in some venues, because I'm aware that many businesses have significant security lapses and often simply no understanding of the problems, much less motivation to tackle them.
In most situations, you can still pay in cash.
As a side-benefit, with cash you aren't directly giving the "vampire squid" of Big Finance its 3 or 5 or whatever percent... "tithe", I guess I would call it, these days.
(And as for debit cards... unless you are forced to use one, as an end-user why would you forgo the additional protections a credit card offers and take on the risk of a direct route to your personal assets?)
I suggest keeping a few $20's in your wallet and paying for things such as Chang's in cash. I'd rather lose $100 in cash, than deal with a breach of my account security.
I recognize that my thinking at this point doesn't encompass what happens to risk if and when we all start carrying more cash around, again, and become as a group sweeter targets for random robbery.
I also don't haul out an obviously loaded wallet or money clip, when paying. No point in "waving" that cash about and thus standing out of the crowd.