If I were the host I would not like it if one of my guests tried to end a conversation with "We'll have to agree to disagree" and the other guest continued with "No, we can't, actually. There's a theorem of rationality called Aumann's Agreement Theorem which shows that no two rationalists can agree to disagree." In my book this is obnoxious behavior.

I'd find it especially obnoxious because Aumann's agreement theorem looks to me like one of those theorems that just doesn't do what people want it to do, and so ends up as a rhetorical cudgel rather than a relevant argument with practical import.