I know the connection sounds obvious. I think there's a definite correlation between authoritarianism and absolutism whether the leaning is left or right. However, in a recent discussion of moral objectivity, it occurred to me to consider what possible difference absolutism might make.
Suppose Rob the moral relativist and Abe the moral absolutist each engage in practices that the other finds morally wrong.
The Rob thinks Abe is committing immoral acts, perhaps due to Abe's personal nature, accidents of history and so on. That is, Rob finds Abe's actions to be distasteful. Rob will take action to change Abe's practices. He will try to persuade Abe not to commit the immoral acts, perhaps by describing the adverse consequences of those actions. Rob may agree to live under a treaty while reserving the right to trying to persuade Abe to change his ways. If the acts of Abe are sufficiently wrong in Rob's subjective view, he may use political measures or force to stop Abe.
How will Abe's actions be any different from Rob's? Even if morality is objective, Abe cannot be certain that he is correct - his must reserve some doubt because it has already been conceded that objective morality doesn't preclude people from being incorrect about it. So Abe will try to persuade Rob to act morally, but Abe may decide to make a treaty with Rob. If Abe has sufficiently strong objections to Rob's behavior, he will try to coerce Rob.
It could easily be argued that Rob and Abe will do the same thing independent of their views on the objectivity of morality.
However, it could also be argued that moral absolutists are less likely to enter treaties (i.e., be liberal). My sense is that holding to views of objective morality makes one less liberal (and more authoritarian), whether one's morality is right-wing or left-wing.
A moral absolutist is more likely to coerce on the issue of abortion or gun control than is a moral relativist. The relativist can be expected to do what he thinks is best, but feels a lesser commitment to abstract principle.
We can see this by analogy to physics and mathematics. There is a form of authoritarianism in science stemming from its objectivity. Repeated experiment trumps personal opinion every time. The principle is that if we can deny empirical fact in one place, then anything can be justified. That's why we don't tolerate flat-Earthers in the scientific community.
Likewise, the moral absolutist is committed to holding the line on every little moral issue, independent of import. If the principle of objectivity can be broken in one place, then what is to stop it being broken elsewhere?
The moral relativist sees morality like taste in food. Gastronomically, there is widespread (though not total) compromise and liberalism. We don't feel that if our friends eat foods we don't like, that it breaks some deep principle, and that if we don't nip it in the bud, people will start eating bicycle chains and pond scum.
Analogously, the moral relativist is more open to differences in moral behavior, as long as they aren't excessively offensive to his sensibilities. For example, the relativist may find abortion to be distasteful, but will not coerce a woman to come to term against her will. As long as his wife or daughter aren't forced to have abortions, the abortions of others do not represent a threat in the form of a challenge to an overarching principle. Similarly, a relativist who dislikes guns is willing to compromise with gun owners as long as his family isn't threatened by gun violence.
I've long been aware of the correlation between liberalism and relativism and between authoritarianism and absolutism, but I don't recall having thought formally about the possible mechanisms linking the two.
Recognition of this connection may prove useful in formulating political compromise.