Sure, they'll move around in the prop wash.

But that's fine, isn't it? If they're intended to detect fixed objects, then noticing that one or more of them have ceased to be blown around in that way may be a good way to detect unanticipated contact with a fixed object: When the signal becomes less noisy, then maybe something is in the way.

And the whiskers don't have to be all floppy like a wet noodle. I myself am thinking that something rigid or semi-rigid might be good. Perhaps something akin to armature wire, or thin spring steel. Maybe even literal bamboo chopsticks.

They can also be constrained so that they don't get sent into the props.

My little brain thinks that the drone-end of the whiskers can be attached to potentiometers, with light return springs to bring them back towards center, like the mechanism used by an analog stick on a PS3 controller.