XRK Audio has kindly shared his measurements without/with SS relays at the output, using VHex+ as the reference amplifier. I also use some text quotes from the original post by XRK.

Some people were skeptical about placing SS relays between the amplifier's output and the speakers, assuming the relays add some distortion. High-precision measurements presented below speak for themselves. The myth is busted! :)

The nominal condition for the test was 14.21V RMS (40.2Vpp) into 8 Ohms or 25W RMS.

Here are the measured distortion components (H2, H3, H4, H5, THD) vs frequency for the case without the SSR Protection in place. These are 1M point data sets and an average of 8 sweeps was used:

Here are the measured distortion components vs frequency for the case WITH the SSR Protection in place, again 1M points and the average of 8 sweeps:

Here is an overlay plot showing the THD of both cases:

Here is a representative FFT for 1kHz excitation at 21.21 Vrms (40.2Vpp) into 8ohms for the case without the SSR Protection in place. Settings were 32k points, Blackman-Harris 7 window, 0.88 exponential averaging:

Here is a representative FFT for the same WITH the SSR Protection in place:

And finally, here is the THD vs the Power in watts delivered to an 8ohm dummy load over a range from 65mW to about 32w. The power was adjusted and I manually connected/disconnected the SRR Protection circuit and replaced the connection with a double-ended male-male Faston spade connector. The power setting was untouched to ensure identical conditions:

At the highest power setting, the THD actually was a tad less with the SRR Protection in place. That is not a typo.

SS relay is an excellent solution for speaker protection systems. Relatively expensive one but very fast and showing no influence on the sound quality.