As they say, engineering is a game of compromise. Pick your poison.
Yes, with relays, there could be ticks/pops depending on how large the waveform you're switching (and at what point in the waveform you're doing the switching.) The same could also happen in switched gain controls. -- for switches, one can use a make-before-break switches -- but these are usually special order items and a bit more expensive than the normal break-before-make switches.
The other option is adding a zero-crossing detector (which is what chips like the PGAxxxx series do), they only switch when the waveform is a few millivolts above/below the zero level. It's not perfect, but minimizes zipper/tick/pop noise.
Of course, one can look for analog multiplexers with built-in ZCD... but then again you compromise on the high Ron resistances, variability/tolerances between parts, and the low analog headroom (13dBu theoretical max., ideal case for +/-5V supply)