Different interpretations of facts are reasonable. Different facts are not. It's a lot like "you're entitled to your own opinions but not your own facts", but

Different interpretations of facts are reasonable. Different facts are not. It's a lot like "you're entitled to your own opinions but not your own facts", but with a somewhat different spin. An opinion is a preference, a feeling. An interpretation is a story that puts the facts together in a coherent through-line. Quantum mechanics is a famous example. The facts are not only the data points of experiments, but the equations. They are sufficiently well-tested to be treated as simple matters of fact, and no physicist disagrees. But there are various interpretations: many-worlds, Copenhagen, consistent histories, "shut up and calculate". They all agree on the outcomes of experiments. They differ in how we think about those outcomes. They all take the equations and say, "This is the part that is important and real, and here is how we understand the rest of it." Unfortunately, we are now accusing each other of ignoring basic facts. At least one side must be right about that; it's conceivable that both sides are. Usually, we resolve such a dispute via democracy, but that breaks down when the disagreement becomes existential.