Philosopher: We should not disapprove of the unearthing of truths that we would rather not acknowledge or that, by their dissemination, might influence society in pernicious ways.
Principle
If there's a truth that we'd we should not rather not acknowledge, → disapprove of or that might influence that truth society in pernicious ways being unearthed if it were disseminated
Evaluate
Writing this principle as a conditional is definitely not necessary, maybe not even recommended. We wrote it that way mainly out of the force of habit that most principles are conditionals. But this doesn't feel as much like a set of instructions for "if this is true, then that is true", and more like an expression of tolerance / values.
The philosopher is saying we should just accept the truth, no matter how ugly or uncomfortable it is.
Unearthing = discovering dissemination = spreading widely pernicious = harmful
If a journalist discovers something that makes us uncomfortable (like drone strikes killing civilians during Obama's presidency), we shouldn't get mad at the journalist for publicizing that.
If we discover something true that would harm society if it became widely known, we should tolerate it.
The truth is the truth. We should accept it and not criticize anyone spreading it.
Goal
Look for something where there's a potentially ugly / dangerous truth, but the paragraph is saying we should tolerate / accept learning this truth and letting this truth spread.