Can an audio rack be that important?

I’d say, like most things we buy, there is a minimum quality standard that should be adhered to. That being said, there are both acoustic and aesthetic advantages to be had if it’s in your budget.

I built my own by repurposing some walnut furniture into a number of shelves that can be configured in a multitude of designs based on where they are placed in the space.

Ive had these as one tall rack, two medium racks and recently into three short racks. Connectors are 3/4" black pipe from Home Depot. Most components are on IsoAcoustics Gaia footers, IsoAcoustics Orea or IsoPucks.

Yes absolutely , you can measure the vibration ,a decent stand today $minimum.  $1500  there are $20 k stands with seismographic control electrically

if you have the bucks ,$500 nothing special , but you can buy the iso acoustic pucks  sold by weight needed and 4 is better then 3  that’s a good stop gap 2-300 per component start with the dac ot digital and or turntable .  They make nice ones for speakers about $600 for 2 speakers .

Yes it is Important.

No, you do not Have to spend a lot of money.... but it Helps.

Thanks guys. 
Prioritizing spending on what makes the most sonic difference can be part of the fun.  I have always tried building or configuring stuff myself like different types of stands, air bladder suspension, lots of cables, and the damped springs I use as footers beneath Sound Anchors speaker stands.   
I try not to get too hung up on the need to spend lots of money to accomplish a goal. For example, a little effort and ingenuity could turn a typical block equipment stand or a flexy stand into something with a unique look.  The stands in the previous post are a good example of how you can make something cool without spending too much. Below are some shelves we recently added as part of a renovation in one of our offices.  The combination of steel framing and aged/cured hardwood boards looks great, and could make a really cool equipment rack, but unfortunately the wood was not cheap.

Like Mike said, pretty close to the bottom of the food chain. At least for my concrete floor setup. It would go considerably up the food chain for my TTs if I had wood flooring on joists.