There are a wide variety of materials and methods for making the propellers used on drones. This leads to certain propellers having different characteristics than others. Some propellers are more flexible than others and I am wondering how that would impact the efficiency of a drone?
It's really a challenging question to answer because flexible and stiff propellers both have their advantages and disadvantages in terms of efficiency.
Flexible propellers are typically lighter than stiff propellers, so they spin-up more efficiently than stiff propellers. On the other hand, when a propeller is spinning at higher speed, a flexible propeller will have a tendency to flex upward and flatten out vs a stiff propeller that is designed to resist flexing (stiff propellers will still flex, but not as much as a flexible propeller). With a flexible propeller, this could result in a scenario where you have more throttle to give, but the drone won't go any faster. To some degree, you might also notice that the drone is less controllable - might not take a corner as well as a stiff propeller would.
If you have a lower powered motor, a flexible (lighter) propeller might be your best option because you may never reach the point where efficiency is an issue. However, if you have powerful motors, and your desire is for speed, then a stiff propeller will probably be more efficient at higher speeds than a flexible one.
Multirotor propellers with too much flex can actually negatively affect thrust generation efficiency, but not in the way you might suspect.
During high throttle punches, the propellers experience significant amounts of stress. If the propeller isn't stiff enough, the propeller can begin to flatten out across the chord, deforming and changing the shape of the airfoil so that it behaves like it has a lower pitch than it actually does, as well as fluttering back and forth and creating more audible noise than usual.
The deformation can even get to the point where the propeller completely flattens and no thrust is generated! This results in decreased efficiency because the extra power spent increasing the propeller speed isn't resulting in as much thrust generation as it should.
Some multirotor propellers are specifically designed to minimize this deformation at high throttle, like the Karearea Aero Blades. These 5150x3 propellers have ribs running the length of the chord of each blade, which has the effect of preventing the propeller from flattening out at high throttle.