Drains backing up - will it affect my drinking water?
Blocked drains have no effect on the safety of your drinking water, if you don't contaminate the supply with the backed up drains.

Any remotely "modern" faucets (and other plumbing) are designed to prevent such contamination - they terminate above the level of the sink, so the end of the faucet cannot be submerged. Those which can be submerged or have a hose attached are outfitted with vacuum breakers to prevent backflow.

Even with a submerged faucet end (from an old faucet), there would ALSO have to be a loss of pressure on the city water to cause any backflow into the supply system.