I lived in SoCal when Prop 65 was passed & the signs were all new. The sign basically means that your apartment contains paint & carpet. The same type paint & carpet as your last apartment in whatever other state had.
Substantially everything plastic or petroleum-based is theoretically carcinogenic. And every man-made structure or vehicle (and many/most common household items) contain those sorts of components, at least in trace amounts.
The law behind the signs was an overly back-to-nature attempt at consciousness raising; to get Californians to recognize the horrors of modern life & return to their chemical-free natural fiber roots. It was expected to lead to a hue & cry to reduce carcinogens in the man-made environment.
Had the law been writen with sensible thresholds, so you could tell the difference between wading into a toxic sludge pile & walking into a Target store, the signs might have done some good.
Instead, the thresholds were set so close to zero that damn near everything qualifies as “carcinogenic.” So rather than doing good, the law simply spawned an industry in posting little signs at the door to every commercial building in the state. And once the signs are everywhere, they’re effectively nowhere; everybody just ignored/ignores them as meaningless.
Every house & car in the state ought to have one too, but the law exempted private residences & vehicles from needing to post signs, no matter how carcingenic their contents.