If we take the distinction between more subjective ("Vanilla ice cream is yucky!") and more objective ("Mongolia is in Asia.") beliefs as a genuine difference in kind, then we must, if we are to be logically consistent, admit that every assertion that something is an objective fact is, itself, a mere subjective belief!
"Well," you protest, "it is an objective fact that the Earth is 93 million miles from the Sun: it's been measured by scientists!"
But did you "measure" your belief that the mileage has been measured? Because if quantitative measurement is the lodestar of objectivity, then your belief that the Sun-Earth distance is an objective fact is itself completely subjective: you can't measure the degree to which that fact was determined by measurement, or, even if you could, you would just be stuck in an infinite regress: you'd have to measure the degree to which the belief in that second measurement was a result of measurement, and so on ad infinitum.
Of course, this is only a problem if one reifies the purely notional distinction between the objective and the subjective: Michael Polanyi, a great physical chemist before he was a philosopher, noted that one can't do this in Personal Knowledge, and idealist philosophers repeatedly showed this distinction is not viable if turned into a difference in kind.