You can have evidence against scientific hypotheses - but not against subjective experiences.
So: the notion of "evidence against quantum immortality" does not seem to make very much sense.
In that case, by conservation of expected evidence the idea of "evidence for quantum immortality" makes about as much sense. In context then, this is just as much of a problem with Pavitra's objection to people interpreting the current state as evidence for.
People around here seem to think that a recent series of near-misses, such as not destroying the world in the Cold War, is evidence in favor of quantum immortality.
This fails to appreciate that the anthropic selection bias has no limit on how far back it can make things retroactively seem to happen. If, as has been suggested, a majority of the Everett branches from our 1950 destroyed the world, then it is equally true that a majority of the Everett branches from our 1750 in which there is someone still alive in 2010 failed to contain probably-world-destroying technology.
The existence of x-risk near-miss events should be taken as evidence against quantum immortality.