Archer, (one of) the founding father(s) of the Federation, is a great man precisely because he is able to grasp that "he is not in Kansas anymore", that this new age requires interspecies ethics and not human ethics.
If they followed the latter they could e.g. eat the Tellarite pigs.
Let's stop dancing around the issue: the PD is nothing but the ultimate expression of the concept that there is no such thing as good/evil, right/wrong, etc, and that all is perspective, and that no one should exercise any sort of moral discernment.
Which is a notion that is total and complete BS. At best it's an excuse for moral cowardice, and at worst it's collaborating with evil.
If I were Central American and were so-inclined as to attempt to revive the Aztec human sacrifice religion of Mezo-America, would you just shrug and say "your culture, your rules...I have no right to judge you or interfere..."?
I seriously doubt it. No person with a functioning conscience would defend permitting that to happen.
In Trek terms, witness the case of Dr Timicin (TNG) and the Eminians/Vendikans (TOS). In both cases their societies had developed socially dysfunctional, if not outright diseased cultures that were committing great acts of evil on the populace. Kirk (rightly) said basically "Oh no you don't!" and did something. Picard, Troi, et al just shrugged and said "it's your culture"and let him go kill himself not because he was facing a horrid, lingering death in great pain, or even because he was some sort of burden, but only because his sick culture decreed that everyone must die at 60.