Spoiler warning, the nature of the infamous "Why man" and origin of the petrification event were both revealed in the new issue of Dr. Stone (chapter 229 for context) so you may be wondering why I'm suddenly comparing what has been jokingly called the Minecraft anime to the crazy action anime where half naked school girls fight each other with giant scissors. The answer is that I see a distinct similarity between the medusas from Dr. Stone and the life fibers from Kill la Kill. Both are space faring parasites that manipulate other intelligent species into helping them with their reproduction, though the Dr. Stone version is less destructive.

Let's compare the life cycles here: The Life Fibers drift through space until they land on a planet that has life on it, then manipulate any intelligent organisms they find into making clothing out of them by granting enhanced abilities, eventually when enough life fibers are made they enrobe the entire planet and then make it blow up, using the explosion as a propulsive force to send fibers throughout the galaxy like dandelion seeds.

Now Why Man: The medusas seek out planets that produce radio waves, since that is evidence of technological civilization, and upon arrival turn the first random species they encounter to stone (that's why the sparrows were turned to stone first.) Then they wait to see which species starts to talk about the petrified species, which proves they were the intelligent ones that produced the radio waves, and turn THEM to stone. The petrification isn't totally permanent, as it can wear off easier if the person has an active mind (remember, the main characters broke out of it by forcing themselves to stay conscious) though it can be sped up with chemical aid, nitric acid or the chemically similar but stronger nitol. The idea is that people would see being petrified as the gift of immortality, so they would seek out ways to maintain and make more of the medusas.

So that is the similarity, both Why Man and the Life Fibers are space fairing organisms that seek out intelligent life to help facilitate their own reproduction, granting a perceived boon as incentive, though so far it doesn't look like Why Man wants to destroy the Earth so we have that at least.