I'd say the last one is the worst case. For we might disagree on facts, but if we both have shared values with respect to which methods and forms of evidence ar

I'd say the last one is the worst case. For we might disagree on facts, but if we both have shared values with respect to which methods and forms of evidence are valid ways of obtaining facts about our shared reality (and which ones are not), then in principle disagreements of fact can be resolved by giving evidence. Eg, if we both agree with the standards of journalistic integrity and can thus agree that certain outlets are reputable enough to publish retractions when they get things wrong, then we can at least agree on facts published in reputable news outlets. But, if we do not have a shared value in the form of respect for the process of journalism, then one side is free to reject any fact they don't like as "fake news", and neither the amount nor quality of news sources cited will ever change this.