Logicism seems only to be widely recognized as objectivist exactly in the case of the objective Bayesians, who add an axiom of completeness and some variation on the Principle of Insufficient Reason.
The mistake in classifying logicists as subjectivists comes from a confusion about the objective component of subjective Bayesianism. The subjective element of subjective Bayesianism is not in the ordering axiomata that they share with logicists (including the objective Bayesians!), nor certainly in the axiom of completeness that the subjectivists share with the objective Bayesians. The subjective element of subjective Bayesianism is in the licensing of supposedly quantified prior beliefs as starting measures of probability.
Logicists such as Koopman (and such as I) do not argue for such license!