Neither Astrid nor Arnbjorn followed the five tenets or the Night Mother, I see no reason why they should have been protected by them. As demonstrated in Oblivion (purification), less important tenets can be overridden by others. Even if Astrid and her followers were truly the Dark Brotherhood and not just a poor imitation, their disrespect of the Night Mother would warrant severe punishment. Cicero may be unstable, but his attacking Astrid for her blasphemy is completely understandable (given that being in a cult full of psychotic murderers is acceptable in the first place). He's the only loyal member of the Dark Brotherhood left, no wonder Sithis doesn't wish him dead.
Sure neither Astrid nor Arnbjorn followed the five tenets to the letter, however given the following tenets:
Tenet 1: Never dishonor the Night Mother. To do so is to invoke the Wrath of Sithis.
Tenet 2: Never betray the Dark Brotherhood or its secrets. To do so is to invoke the Wrath of Sithis.
Tenet 3: Never disobey or refuse to carry out an order from a Dark Brotherhood superior. To do so is to invoke the Wrath of Sithis.
Tenet 4: Never steal the possessions of a Dark Brother or Dark Sister. To do so is to invoke the Wrath of Sithis.
Tenet 5: Never kill a Dark Brother or Dark Sister. To do so is to invoke the Wrath of Sithis.
At the point where you have the choice to kill Cicero, there is nothing to suggest that the guild had not followed these tenets. In fact, it seems the only one the guild as a whole may not have followed exactly was #1, and to be fair once you became the listener, Astrid didn't seem too keen on disobeying the Night Mother's order to find the contact and subsequently fulfill the contract.
Aside from that, there are a number of other consequential bits to the story of Cicero himself. If you go through Cicero's journals, he seems to indicate he is no longer allowed to kill as his duty is now as the Night Mother's keeper. He directly supercedes this rule by taking up arms against his guild mates. Not only that, but the Old Ways seem to be destroying the guild (Skyrim's sanctuary is the only Dark Brotherhood organization left), a destruction in which Cicero's actions directly support.
Again, I could see myself going either way with this. Yes, Astrid was a blasphemer in the eyes of the Night Mother and Sithis, but to what true extent? Wouldn't Sithis have already stepped in by now to right the error of her ways instead of waiting until this was the final sanctuary? Maybe, maybe not. I took this as a sign on my first character that the survival of the guild as a whole should take priority, not the life of one ultimately inconsequential mad jester.
On my next character I plan to keep him alive as this will actively be part of my Vampire Battle-Mage's role playing tendencies.