Setting aside the pejorative (or friendly) quality scientism [EDIT]( or positivism for that matter)], I am unclear about the issue raised here. Why would just having an epistemology necessarily mean the activities based on it are inherently self-refuting (*1) ?
Consider that anything we think about has to have an underlying "world view." Be it science, religion - or the art of cooking cheeseburgers, everything
is underpinned by the human methods of thinking. So science must have an epistemology - or science could not even be science. (Sure, there may be more than a few unthinking scientists, but that's another fish to fry.)
The OP seems to be addressing folks who, to me, are raising a false philosophical dilemma. Or better said, are presenting a form of the mind-body problem conflated with the "three blind men and the elephant" story.
Consider: science can be only as objective as the thinker. (Who may or may not be a scientist.)
Thought is its own solvent.
(*1) If we have come to think that epistemologies are inherently UN-objective, and if that stance is truly indicative of philosophy today, then we've all already been to hell in frayed hand baskets.