"if turning on the LHC or other world-smasher causes other probabilities to behave oddly"

How can it possibly do so, except in the plain old sense of causal interaction, which is emphatically not what this discussion is about?

Let's think about what observer selection effects actually involve.

Suppose that there is a sort of multiverse (whether it is a multiverse of actualities or just a multiverse of possibilities does not matter for this analysis). At some level it consists of elementary "events" or "states of affairs" which are connected to each other by elementary causal relations. At a slightly higher level these elementary entities form distinct "worlds" (whether these worlds are strictly causally disjoint, or do interact after all, does not matter for this analysis). At some intermediate level are most of the complex entities and events with which we are habitually concerned, such as the activation of the LHC and the destruction of the Earth.

Regarding these intermediate events, we can ask questions like, what is the relative frequency with which event B occurs in a world given that event A has occurred elsewhere in that world, or even, what is the relative frequency with which event B is causally downstream of event A, throughout the multiverse? (Whether the first question is always a form of the second, in a multiverse which is combinatorially exhaustive with respect to the elementary causal relations constituting the individual worlds, I'm not sure.)

So far, so straightforward. I could almost be talking about statistical analysis of a corpus of documents, rather than of an ensemble of worlds, so far.

Now what are observer selection effects about? Basically, we are making event A something like "the existence of an observer". When we condition on that, we find that some Bs become significantly more or less frequent, than they are when we just ask "how often does B happen, across the multiverse?".

But suppose my event A is something like, "the existence of an observer who reads a blog called Overcoming Bias and shares a world with a physics apparatus called the LHC". Well, so what? It's just another complicated state of affairs on that intermediate level, and it will shift the B-frequencies from their unconditioned values in some complicated way. Even if there are subjective duplicates and their multiplicities change in some strange way, as in an interacting many-worlds theory with splitting and merging... it's complicated, but it's not mysterious.

So finally, what is the scenario we are being asked to entertain? State of affairs A: The existence of an observer who shares a world with an LHC which repeatedly breaks down. And we are asked to estimate how this affects the probability of state of affairs B: An LHC which, if it worked, would destroy the Earth.

Well, let's look at it the other way around. State of affairs A': An LHC which, if it worked, would destroy the Earth. State of affairs B': An LHC which keeps malfunctioning whenever it is switched on.

From this angle, there is no question of anthropics, because we are just talking about a physics experiment. All else being equal, the fact that something is a bomb does not in any way make it less likely to explode.

If we then switch back to the original situation, we are in effect being asked this question: if a device keeps breaking down for unlikely reasons, does that make it more likely to be a bomb?

The sensible answer is certainly no. Now maybe someone can come up with a strange many-world physics, in which observer-duplicate multiplicities vary in such a way that the answer is yes, on account of observer selection effects. It would certainly be interesting to see such an argument. In fact I think this whole line of thought originates with the fallacy of conditioning on survival of observers rather than conditioning on existence of observers. (Even if you die, you existed, and that uses up the opportunity for anthropic reasoning in the classic form.) Nonetheless, some wacky form of observer-physics might exist in which this generic conclusion is true after all. But even if it could be found, you would then have to weigh up the probabilities that this, and only this, is the true physics of the multiverse. (And here we hit one of the truly fundamental problems here: how do we justify our ideas about the extent of the possible? But that's too big a question for this comment.) If only one little corner of the multiverse behaves in this way, then the answer to the question will still be no, because A and B will also occur elsewhere.

So, to sum up a long comment: This whole idea probably derives from a specific fallacy, and it should not be taken seriously unless someone can exhibit an observer-selection argument for a breakdowns-implies-lethality effect, and even then such an effect is probably contingent on a peculiar form of observer-physics.