How important is an audio rack?

If it will hold your gear without collasping or bending or leaning to one side, then, it is a good rack. Appearance is up to you. Thats all a rack does. Period.

"One store owner/salesman stated the audio rack should be considered the most important component, even with a very modest system!" What a bunch of bs. Walk away.

If it holds your stuff securely and does not ring like a bell its fine. If you want to spend more money for aesthetics, that is a different and personal choice.

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.