How important is an audio rack?

Aesthetically, perhaps important to some.

Regarding sound quality, its important that it be built solidly enough to serve as a rigid foundation. I tend to like low profile racks or shelves for this reason. Cheaper and most effective. Tall, vertical units are more problematic and cost more to do right. Equipment that sits higher up off the floor will tend to be subject to vibrations of greater magnitude, like a high rise in an earthquake.

I also tend to prefer wood construction in that the damping characteristics of wood is generally quite good compared to other materials, say metal or glass.

That's about it.

Its also imporant that the floor it sits on functions well as a rigid foundation. Concrete foundations work very well. Upper levels of homes, especially newer ones, are more problematic.

How much all this matters of course depends on the quality of the system and the needs of the listener. Many will not give a hoot in practice. In my main rig, I care. In my second 2 channel A/V system, I do not care. WAF matters more. That second system still sounds fine.
Can't match my main rig though in critical listening comparisons.

"an extreme audiophile I visited had sturdy metal racks; the kind you see in Stereophile. Since his sound was the best I've heard, I know they make a difference."

Maybe, but I'd wager the rest of the gear and the setup as a whole had a lot to do with it.

I guess one would have to switch racks and a/b compare to know for sure.

The audio rack/stand/isolation ante is much higher with turntables in particular than with other gear. Other mechanical devices, like CD players, maybe.

For amps, pre-amps, etc., I'd focus on isolating each component from external EM or RF noise/fields, including those from other components. Low level phono circuits are also most susceptible to these as can be CD players and any line level gear.

The easy solution is to provide space between components, especially between phon and line level devices and power amps. ALso keep away from eletrical appliances, etc.

PRoper isolation is important for really good sound. Its often not as complicated or need be expensive as some may make it seem.

The quality of the rack will not matter much if some of the other considerations for effective isolation are not taken into consideration prior.

It could be a total waste of money without looking at the big picture from an isolation and vibration perspective first, or a relatively inexpensive solution could turn out to be the cats meow.

Also, the considerations are different for what is needed to isolate a turntable effectively compared to digital gear. If you have both, then two separate sets of considerations to address come into play.

"I bottom load all components using large Tupperware-styled containers filled to the brim with dry beach sand. "

Very creative, and I would guess also most effective!

I'm assuming you use audiphile grade Tupperware containers which of course are way more difficult to construct properly for best sound and sell for a premium as a result. :-)

It's very important to dealers due to relatively high markup/profit margin compared to actual electronic gear I'd bet.

A solid foundation to support gear is important to keep it stable, especially components with physical moving parts that directly impact sound like a turntable. A solid foundation never hurts. It's an insurance policy at a minimum. Search audiogon threads for lots of good info on the topic.