Speakers hung from ceiling on aircraft cable.

Opinion question:

We are thinking of suspending a pair of KEF LS50 speakers from the ceiling using aircraft cable. Do you think having them not rigidly mounted will diminish bass? Will the woofers cause the speakers to move?

You could try mounting them on a ceiling mount pole designed for TVs. Or something like that.
The only way to hear if the loss is acceptable is try it.
This is a practice used in baffleless dipoles for bass and midrange drivers,  where the drivers hang on a swing, however generally not suspended from the ceiling but a frame.

Doing without the baffle avoids vibrations transmitted to the panels. Of course this requires significant eq because of the 6 dB/octave slope before the dipole peak, which is where the drivers should be operated. I'm experimenting with this now.

Anyway, probably not doing much hanging boxed speakers in a swing.
If you have the right speakers yes. Mine are hanging fine. 15 year's now. There also inverted with springs, between the cables. Then you build soffits around the monitors.  There is a very good reason why very hi end recording studios (mount) there monitors in this fashion.  One is bass, two imaging, three is woofer bounce, from the floor. That is my experience.  :-)
I had a Mini Utopia speaker suspended from 4 piano wires behind a perforated drop screen in a multi purpose home theater for 5 years.
Worked fine crossed over at 50 HZ.