Thanks for the question -- it's important to grapple with even though it can be very uncomfortable and answering it is basically one can of worms after another. If you entertain it seriously, it really gets down to the philosophical roots of how to treat others from different moral systems and worldviews.
I don't think this is a problem any society has ever elegantly solved, definitely not permanently, and I think it's a distinct possibility that a solution that feels "clean" the way good software design can is not possible.
Abstractly, a culture consists of core tenets that it considers literally unquestionable. For most of history, this list of tenets would include things like the existence of a god or gods, the moral imperative to respect the rulers, the prohibition of things that were thought to harm the group such as murder, theft, or adultery, and so on. More recently in the Western world, we might include things like "women are equal to men" or "people of all races are equal".
It is very difficult to defend these types of propositions and values in any sort of universal or non-self-referential way.
Even things we assume to be moral universals in the Western world like the sanctity of the individual (bodily integrity, freedom of conscience) or the importance of intent in our judgment of wrongdoing (manslaughter vs. murder) are, if you examine the historical and anthropological record, not actually universal at all. (Check out The WEIRDest People in the World by Joe Henrich if you're curious about these specific points.)
The US Declaration of Independence is a classic example of this. It asserts: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
If you don't also find those truths self-evident, all following reasoning based on their axiomatic status might very well seem wrong to you. What if you contest the existence of a creator? What if you contest the idea of innate equality of rights and dignity? What if you contest the focus on rights rather than obligations? Or what if you assert the existence of a different creator who explicitly singled out one tribe as the most holy, righteous, intelligent, etc.?
Because the core tenets of a culture are to some extent arbitrary and thus susceptible to replacement with a different set (like Christianity displacing paganism or atheistic rationalism displacing Christianity), there is a strong inclination to defend a particular set of tenets by making questioning them a taboo. That's the underlying purpose of the concept of heresy and its accompanying social shaming.
Unlimited viewpoint diversity does actually threaten the continued existence of a culture if its defenders are not able to meet the arguments of its critics in a way they and their audience find compelling. If you say "I think gays shouldn't marry because it goes against God's will" and your audience mostly thinks "I don't believe your God exists, so that's an absurd argument", you won't convince very many people and soon people will stop adhering to a core tenet of your culture, perhaps eventually leading to the death of that culture altogether.
In the Western tradition, the probing of a culture's foundational values and assumptions has been the domain of philosophy at least as far back as Socrates being sentenced to death or exile for showing impiety toward the gods of Athens and corrupting the city's youth by prompting them to ask questions that must not be asked.
So what does this rambling mean for toleration of viewpoint diversity?
Its absence can prolong injustice (abolitionists faced lots of censorship in the 19th century) and undermine scientific and creative inquiry (see Socrates, Galileo, McCarthyism, etc.). At the same time, its presence leaves all of your holy cows, carpenters, and civil rights vulnerable to ideological attack.
Those are two difficult tensions to reconcile.
I come down on the side of erring toward more viewpoint diversity because I think it encourages reflection into why you hold the values you do and teaches you to defend them vigorously or, sometimes, change them to something you find more compelling.
This isn't something everyone wants to do all the time everywhere, though, so I understand not wanting your company's Slack to devolve into constant philosophical debate or even less productive forms of disagreement.
I think we've been running into such trouble with this recently because many of the existing implicit boundaries separating parts of our culture were washed away by the great cultural homogenization of the internet and especially social media platforms. It used to be more possible to have fierce debates on university campuses about contentious issues without that instantly bleeding over into industry, non-profits, schools, knitting clubs, etc.
It's like Douglas Adams wrote: "the poor Babel fish, by effectively removing all barriers to communication between different races and cultures, has caused more and bloodier wars than anything else in the history of creation."
Sometimes boundaries are healthy.
The best answer I've encountered is moving in the direction of a more federal system in which cultures can live as they think best AND individuals in each culture are empowered to move to different cultures if they don't like where they are.
This is not a perfect solution, though, because it still requires the universal enforcement of certain moral propositions, like people should have the right to their own body and mind and choice of home. Those propositions would not have been accepted in slave-holding societies or even recent collectivist societies like the USSR, which prohibited its citizens from emigrating without permission. This is, realistically, an iterative improvement that would only apply to cultures that already accept foundational Western moral attitudes.