Are Toxic Political Conversations Changing How We Feel about Objective Truth? makes the important distinction between arguing to learn and arguing to win. Research has shown that the way you pursue an argument will also affect the way you actually think about the issue at hand, i.e. the degree to which you believe there is an objective answer or not:
So the next time you are deciding how to enter into an argument on Facebook about the controversial question of the day, remember that you are not just making a choice about how to interact with a person who holds the opposing view. You are also making a decision that will shape the way you – and others – think about whether the question itself has a correct answer.
I tend to think that objectivist perspectives are also simply easier and faster to communicate than relativist ones, which puts the latter at a natural disadvantage in the typical social media discourse that often feeds on outrage or quick reactions.