How should we respond to disagreement?

The problem with this is that if the rational response to disagreement (where your interlocutor is equally intelligent, equally well-informed, etc) is to suspend judgement, and you refuse to suspend judgement more than 0.01% of the time, then you're much more irrational than you present yourself as being. Let's say that in 1% of the debates you have with intelligent, well-informed interlocutors, you refuse to suspend judgement. Then, for somebody who accepts the conciliatory view, you're 10x more irrational than you claim. So I don't think it's good enough to respond to the conciliatory view by saying that you're happy to be irrational on occasions few and far between.

In my view, there are persuasive arguments against the conciliatory view. The most important one for me is that it's self-undermining. Most people who defend it will try to provide arguments for it - certainly, if you want me to adopt a substantial epistemological principle like this, you'll need to provide a convincing argument. The horse race analogy might be reconstructed as an argument along these lines:

(1) It is irrational to retain your belief that horse A won.
(2) So, if there is no relevant difference between the horse race disagreement and weightier disagreements, then it is irrational to retain your beliefs in cases of weightier disagreements.
(3) There is no relevant difference between the horse race disagreement and weightier disagreements.
(C) So, it is irrational to retain your beliefs in cases of weightier disagreements.

The problem is that for any argument you give for the conciliatory view, you can be sure that there will be intelligent, well-informed who disagree that the argument provides persuasive reason to accept the conciliatory view. So, if you accept the conciliatory view, you must suspend judgement about the force of your argument. So the conciliatory view is self-undermining: once you adopt it, you are forced to accept that none of the arguments for it are good enough to persuade those who hold a different view.

Of course, it's possible that a defender of the conciliatory view will one day offer an argument that every intelligent, well-informed person will find persuasive. But I think that an induction on the history of philosophical debates suggests that this is extremely unlikely.

Yeah it does seem a bit self-refuting.

To clarify then: I was using the phrase "the conciliatory view" to refer to the view that it is irrational to retain your belief when you encounter disagreement from people who are equally intelligent and equally well-informed.

It would require you to suspend judgement about which music is better and which food is better. This only concerns beliefs. If you believe the proposition "Frank Zappa is better than Bob Dylan", and you encounter somebody who is equally intelligent and well-informed who believes the proposition "Bob Dylan is better than Frank Zappa", then you would have to suspend judgement about which is better. But it's perfectly fine for you to go on listening to Frank Zappa and not Bob Dylan. You would just have to accept that there is no reason to think that Frank Zappa is really, objectively better than Bob Dylan.

Of course, for those of us who are antirealists about value, this example is confused. In my view, all such statements of the form "X is better than Y", "X is good", "X is bad", etc, are really just expressions of personal preferences; they do not describe objective facts about the world.