She could pay cash. It is the right of the store owner to refuse service to avoid a fraudulent check. The state issued photo ID serves as a way to verify the identity.
How do they handle passport photos?
Can she walk freely into a bank with her face covered? The upcoming protest in NYC about the WTO has a ban on masks. Would she be permitted to walk through the area with her identity shielded?
I haven't used my photo ID to write a check in years.
My grocery has its own card. Other stores accept various combinations of ID (e.g., a credit card and voter ID.