i don't know, I think the new criticism didn't deny that books were written by specific authors, the authors had intentions in their minds, wrote in a historical context, and so on -- they just felt it was not interesting or fruitful to consider those things when trying to make sense of how a text worked.
at the same time, it's not like they just thought you could make up whatever bizarre misreading you wanted about the text -- you had to present some kind of convincing internal evidence for your reading. even the standards of new criticism rule out a lot of interpretations.
as an outsider it seems like there's a lot of debates in humanities fields that are like that -- what perspective gives the best view of things? what is worth talking about? what kind of evidence and argument is acceptable and convincing?
but it's almost always the case that there are standards, even if people within disagree on them and even if there's no hope of getting to one objective truth.
(there's a lot of very dubious and poorly-done literary criticism, but the same is true of every STEM field.)