Husk, 66 4 bytes
-2 bytes thanks to Razetime!
Von1LgETC2 Hooray for all ASCII solutions! Outputs 0a positive number if the input is doublespeak, otherwise a positive integer. if you want 1 for truthy, 0 for falsey, you can prepend =0 to the codezero.
g C2 Group theCut inputlist into listschunks of the same adjacent elements2 V Find the index of the firstT element that matches the predicateTranspose o E Combination of the next twoCheck functions if list has all Lthe same elements The(return length n1 Is oddof (bitwiselist ANDif 1so)