DaasYochid: I am not sure why you consider the election of a Chief Rabbi- or any rabbi, for that matter- a halachic matter? Most of the reasons are subjective, not objective.
PopaBarAbba- You may say that everyone agrees to what I wrote, but that is not the case. Continually, you hear that it is “daas torah” about a subject and therefore, not to be disputed,making our Rabbonim infallible- which they are not.
zahavasdad- it is not stretching the halacha to be “meikel’ in matters of mamzerus. It is the halacha: “mamzerus vadai omar rachmono velo mamzerus sofek”. Only the certainty in cases of mamzerus is accepted.If there is a doubt about mamzerus, you rule that is not mamzerus.