I submitted a rules question and got a really fast answer from Damon Stone:

Q: Station Eismitte + Dr. Carson: Is his Action triggerable because of Eismitte? (Dr. Carson has to be exhausted as a cost, and I'm unsure if costs are prevented through immunity, too.)

A: Correct. Paying a cost is a player action not a card effect.

Q: Is the Claret Knight's Response ever usable? (It's a triggered effect, and he's immune to such effects due to his passive ability. Erratum?)

A: A card can never be immune to its own effect.

Q: Station Eismitte will prevent a Reckless Elder Thing from wounding itself?

A: Reckless Elder thing would be wounded

I have a question. Does Station Eismette protect vs sacrifice effects, like from Cthulhu or Cthyla character?

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Secret Spawn of Cthulhu
Type: Character Faction: Cthulhu
Cost: 5 Skill: 5 Icons: (T)©(A)(A)
Game Text:
Ancient One.
Invulnerability. Villainous.
Action: Sacrifice a character to have each opponent sacrifice a character with a printed cost equal to or greater than the character you sacrificed. Limit once per phase.
Flavor Text: Should Cthulhu ever be destroyed, he will be reborn through Cthylla.
Set: SoK
Number: 45
Illustrator: Lin Bo

Lord of R'lyeh
Type: Character Faction: Cthulhu
Cost: 6 Skill: 8 Icons: (T)(T)©©(A)
Game Text:
Ancient One.
Villainous. Invulnerability.
Action: Pay 3 to force each opponent to choose and sacrifice a character.
Set: TWB
Number: 64
Illustrator: Jeff Himmelman

I think the key to find the answer is to check if the triggered character ability actually targets one of the characters protected by Station Eismitte.

Based on that, I think they are not protected from Cthylla's ability. Cthulhu's ability, however, requires you to choose a character, so because of Eismitte you cannot choose an Explorer or Scientist. Of course, if you have any character that is neither an Explorer or a Scientist, you'd have to choose that character.

Question:

I have the card Station Eismitte in play. My opponent has the card Cthulhu and all my characters are Explorer and Scientist. If my opponent uses his Cthulhu's action, should I sacrifice a character?
And if instead of Cthulhu has Cthylla, what would happen?

Answer from Damon Stone:

Nothing happens. The owner is not able to choose/target them. If there are no legal targets to be chosen the effect cannot be triggered at all. Also those effects cannot resolve on a character who is immune to character abilities so even if targeting was allowed they still could not be resolved on.

Hmm, I had forgotten that Damon had already provided an answer to bsaically the same question in post #18.