No, it's not physically possible to do any significant active cancellation of the noise caused by a rotor / propeller spinning through the air. The noise sources are too spread out (especially with multi-rotor designs) and cover too much of the audible range.

Blade shape can be tuned to an extent for minimizing noise but that also reduces efficiency (not much to spare). Larger, slower turning blades are also quieter but there are practical physical limits on size and weight.

Aren't flying cars going to be much noisier than surface cars?

Joby is using some low noise props that are very effective. Quieter than most of the ridiculous motorcycles and loud cars on the 101.

If we care about noise, we should be addressing the motorcycle industry. I can’t hear a C-130 flying overhead at 1000 feet when I am in my house, but I can hear motorcycles zipping by on the freeway behind my house.

Yes, that was my point. We will need some clever tech to make the noise bearable.