I think a mechanism that, first of all, promotes some kind of interaction between fields and helps counterbalance the hyper-specialization our academies currently promote.
It is very unlikely that "the academic fields in question demonstrably have no interest in whether things are true or not". More likely is that people from hyper-specialized fields use different criterion for the validity and veridicality of statements and that their incredibly hermetic jargon and deep reliance on interlocking field-specific concepts prevents them from communicating with other academics from other disciplines in meaningful ways—thus resulting in a great sense of misunderstanding and misjudgment between members of the fields. In some sense, our pursuits are so hyper-specialized at this point that they are incommensurable—there's an incredible lack of 'generalists' able to act as liaisons and to produce the appropriate meta-criticisms for each field of study.
That, I think, is a much more reasonable assumption than one that assumes a cohort of people who "don't have interest in the truth" have somehow slipped their way into academia and are using it as nothing more than a vehicle for their political motives—that's a rather conspiratorial hypothesis and would need much more evidence to support it than the publication of a couple of papers in a couple of journals.
If we were to solve the hyper-specialization problem to a degree, I think it would promote greater academic health and collaboration overall.
> It is very unlikely that "the academic fields in question demonstrably have no interest in whether things are true or not".
Er, they are actually quite open about this.
For example:
Founded in 1974, the Michelle R. Clayman Institute for Gender Research at Stanford University has put research into action by inspiring innovative solutions that advance gender equality.
The goal/purpose is "advancing gender equality", not "truth finding".
Most of these fields don't just not believe in truth as a concept, they actually actively oppose and dismiss the search for truth or requirements for evidence as being expressions of and mechanisms for maintaining illegitimate power hierarchies.
Now hyper-specialisation is also a problem, but it's not this problem.
So what is? Specifically, what is, given that the academic fields in question demonstrably have no interest in whether things are true or not?