Two ideal Bayesians cannot have common knowledge of disagreement; this is a theorem.

To quote from AGREEING TO DISAGREE, By Robert J. Aumann

If two people have the same priors, and their posteriors for a given event A are common knowledge, then these posteriors must be equal. This is so even though they may base their posteriors on quite different information. In brief, people with the same priors cannot agree to disagree. [...]

The key notion is that of 'common knowledge.' Call the two people 1 and 2. When we say that an event is "common knowledge," we mean more than just that both 1 and 2 know it; we require also that 1 knows that 2 knows it, 2 knows that 1 knows it, 1 knows that 2 knows that 1 knows it, and so on. For example, if 1 and 2 are both present when the event happens and see each other there, then the event becomes common knowledge. In our case, if 1 and 2 tell each other their posteriors and trust each other, then the posteriors are common knowledge. The result is not true if we merely assume that the persons know each other's posteriors.

So: the "two ideal Bayesians" also need to have "the same priors" - and the term "common knowledge" is being used in an esoteric technical sense. The implications are that both participants need to be motivated to create a pool of shared knowledge. That effectively means they need to want to believe the truth, and to purvey the truth to others. If they have other goals "common knowledge" is much less likely to be reached. We know from evolutionary biology that such goals are not the top priority for most organisms. Organisms of the same species often have conflicting goals - in that each wants to propagate their own genes, at the expense of those of their competitors - and in the case of conflicting goals, the situation is particularly bad.

So: both parties being Bayesians is not enough to invoke Aumann's result. The parties also need common priors and a special type of motivation which it is reasonable to expect to be rare.