How important is an audio rack?

Every material and construction has its own resonance signature. That's why you find turntable plinths, platters, and arms of acrylic, aluminum, magnesium, and so forth. Some tables are mass loaded, others light and rigid. Same thing with speaker cabinets, baffles, and drivers, all with different materials and construction. There are many different flavors and many ways to success or failure.

If you don't think it makes a difference, you are mistaken. If you can't hear a difference, I can't argue with that.

That store owner certainly seriously exaggerated the matter but I wouldn't necessarily walk away.

If your gear is that prone to resonance and vibrations maybe your using the wrong gear.

Rhljazz:

Or, on the other hand, it could just all be marketing. Its seems like the people that say all these things are the very people that sell all these things.

Oh, how I long for the good days, before we knew about racks and wire and the doo hickies to hold the wire off the floor. Back in those days folks actually listened to music.

If your gear is that prone to resonance and vibrations maybe your using the wrong gear.
Gshepardbuster

Actually, it's the other way around. The higher the resolution of the component, the more likely you are to hear a difference. Not so much a problem for mass market and mid fi components.

Very few products at any price attempt to address internally generated harmonics or reduce externally transmitted vibration. Some CD players have sprung transports for example. There are amplifiers with floating circuit boards and Berning even uses Stillpoint devices in some of their amps to isolate the boards. Some of the casework on my VAC preamp is damped but it still is not immune to the stand or the room. All transformers create noise.

I generally find I like Stillpoints and spikes (although I don't buy into the vibration draining theory, whereby every resonance in the component is grounded through the spike)

Racks are expensive to try out, but maybe trying some of the footer tweaks would prove enlightening.