I like this idea...a lot. If I may ramble...
Mushroom Sci-Fi embraces the fact that the future is unpredictable. We can't predict future science and technology as we try to do with Hard Sci-Fi. It's like a bronze-age farmer trying to predict an autonomous combine harvester. We can't take for granted that present day themes, morality, desires, etc. will be the same in the future as we do with Soft Sci-Fi. We no longer wage war for sake of personal honor or perform ritual animal/human sacrifice, but some bronze-age aspiring Soft Sci-Fi author probably would not have considered that. And that's only 3000 years ago!
Mushroom Sci-Fi throws out the idea of trying to predict future science and technology or show that human stories are timeless. (But, regarding the latter, there's only so much of present day themes etc. that you can toss before it becomes uninteresting to the present day reader.)
I would offer up Zardoz and Fantastic Planet as two examples of Mushroom Sci-Fi.