Let's try a few scenarios.
I'm white, have been working in my garden, and want a drink. I walk through a park and playground to the corner store to buy a soda. I have $5 and my house key, but no documents. I'm probably safe.
Same scenario, 3rd generation hispanic american, born in this country. Is safe from this law in theory, but may well spend a night or two in jail until they can prove they are a citizen.
Likewise asians or anyone with an accent.
Giving police the ability to stop anyone on suspicion of being an illegal alien invites abuse of power.
As for the check list above, they're all moot points. Those are generally privileges denied illegal aliens anyway, and you're expected to provide that information. I don't need an ID to exist. Biking, shopping, walking, just about anything done in a public place can legally be done without identifying documentation. Thanks to this law, if you're not white, you don't dare do these things without documentation, even if you are a legal citizen. Therein lies the problem. This law infringes on the rights of legal citizens who happen to be Hispanic or foreign looking.