The ultimate arbiter of truth is experiment, not the comfort one derives from one’s a priori beliefs, nor the beauty or elegance one ascribes to one’s theoretical models. - Lawrence M. Krauss
Actually, the ultimate arbiter of truth has to be subjective in nature because purely objective entities or processes cannot arbitrate among or between anything.
Experiment relies upon the subjective experimenter to determine the conditions and variables and then the interpretation that follows. Ultimately, your view relies upon the assumption that “objective” reality is only objective and nothing more.
Using a literalist interpretation of text, as a parallel or analogy, your “objective” approach rules out a priori that there is anything more than a literal level contained in the narrative. The problem is that this approach becomes self-fulfilling and self-authenticating if the narrative is consistent at a literal level.
In the case of science, “objective” means objective to the observing subject, which, is still an aspect of the observer’s subjective viewpoint. The observer has merely convinced themselves that their inherently subjective viewpoint actually “gives way” to an objective one, which is not necessarily the case.
A literalist who is reading Shakespeare can still make sense of the words taken at their most basic literal level and they may find all kinds of confirmation from the text of the adequacy of this level of interpretation, but that is a kind of “blindness” to what is really going on in the narrative at other more symbolic levels.
In order to correct this blindness, it is necessary to demonstrate, first, that words can have multiple meanings and that the most basic meaning of any word is not the only possible one.
This may, very well, be true of natural phenomena. Yet, like the literalist, it could be difficult to convince someone who has worked out a coherent “literalist” interpretation of nature, that, while this interpretation is consistent with the facts it is only a “limited” view of the complete narrative.
There must be a means to separate objective from subjective, or any understanding is on shifting sands, as demonstrated amply by the hundreds of incompatible philosophical -isms.
Your statement assumes that the term “objective” has some meaning apart from the subjective observer. That may, in fact, be delusional. It is not clear, at least not to me, that “objective” has any such “external” reality. Meaning may, ultimately, only be subjectively possible and depicting some imagined external material reality as necessarily “objective” may be setting up a false dichotomy, one which the “facts” support, but taking too literalist a view of the “facts” may serve to mask out more important realities represented in the facts.