What does “sterile stuff favored” means?
I think , It means : It’s a stuff which has none goal , not continuation .
Thank you AGISSON, that helps a lot 
“the sterile stuff favored by most schools” = the sterile stuff that is favored by most schools = the sterile stuff that most schools favor
‘favor’ means ‘prefer’ : Most schools prefer to buy the sterile stuff.
I think what he means by “the sterile stuff” is brand new “clean” furniture that you can buy at chain furniture stores, such as IKEA — as opposed to old, used, sometimes antique, “dirty” furniture that you can buy at thrift stores or at a flea market.
“favored by” is passive voice. If something “is favored by” someone, that means that someone favors something.
active voice: Most schools favor the sterile stuff.
passive voice: The sterile stuff is favored by most schools.
active voice: Most schools prefer brand new furniture.
passive voice: Brand new furniture is preferred by most schools.
in other words:
In fact, funky fabulous furniture can be bought from thrift stores for a fraction of the cost of the brand new furniture that is preferred by most schools.
In this context, I would say that “sterile” implies not only “clean” and new, but also boring, conventional design.
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Absolutely. I totally agree with kewms’s much more insightful interpretation of “sterile.” Sterile not only means totally clean but figuratively implies things that are uninspired and lacking in imagination and creativity, i.e. utterly conventional and utterly boring. The polar opposite of funky and fabulous:
In fact, funky fabulous furniture can be bought from thrift stores for a fraction of the cost of the conventional boring furniture that most schools prefer.