Here another workaround that may be safe (as it would likely affect only expressions containing u'):
ComplexExpand[Null]; (* autoload ComplexExpandDump *)
Block[{System`ComplexExpandDump`ConjugateFunctions =
Append[System`ComplexExpandDump`ConjugateFunctions, u']},
ComplexExpand[u'[t]]]ComplexExpand[{Re, Im}[u'[t]] // Through]]
(* {u'[t], 0} *)