Postmodernism isn't anti-science, it's anti-modernism. Postmodernism doesn't care about science aside from the fact that it happens to make claims to objectivity, which postmodernism disdains. This is sort of like arguing that relativity is anti-science because it denies the existence of a privileged "objective" or "universal" reference frame.

To put it another way: if modernism was actually true and science was an inherently objective process that produced universal truths, then why do we have persistent and ongoing replication crisises in multiple scientific disciplines? Our answer has to come from postmodernism: the current scientific establishment values the production of papers as a way to fill magazines, and people with agendas to push (e.g. the American sugar lobby) will fund the production of scientific papers that produce the answer they want. If that makes sense to you, then you're a postmodernist.

Science has been rewarding politics (e.g. securing funding) over achieving objective truths. Objectivity is a modernist value, and proposing ways how to systemically change society to advance modernist values is something we've been doing for hundreds of years. On the other hand, postmodernism tends to criticize the pursuit of objectivity while embracing subjectivity.