Yes and No
There are really two questions here: would it be possible to handle the Immaterium better than an authoritarian society (e.g., the Imperium of Man in the inspirational material), and whether it would be possible to handle the Immaterium at all. Here's some points to consider from someone who is a bit familiar with the dynamic you're talking about.
The answer to this is rather simple: a democratic society would not handle the Immaterium better than an authoritarian one, but it wouldn't handle it worse, either. Rather, there really isn't a form of government that can reliably handle the Immaterium at all due to the Immaterium exploiting universal flaws in human nature rather than societal structure.
Indeed, in 40k itself the authoritarian nature of the Imperial government does not handle the Immaterium very well. Consider that little in 40k is actually presented from an omniscient third-person perspective; virtually all of the protagonists are human Imperials and thus make decisions and commentary from their cultural perspective (which is "the Imperium is always right", going back to the Great Crusade). Thus, they are going to claim that the Imperial method is "the only way" because it's what they've been indoctrinated to do.
Overall, the extensive body of thought experiments 40k literature has regarding the interaction between society and the Immaterium shows that ultimately authoritarian versus democratic governments are ultimately a wash. The authoritarian Imperium is good at identifying and destroying Chaotic incursions when they do happen, but ultimately their policies result in the average person living in the kind of misery that would lead them to turn to Chaos in the first place. There are even direct quotes from one of the primarchs, Roboute Guilliman, saying exactly this.
Additionally, their intolerant policies cost them allies against the Immaterium (even allies of convenience) as well as causing many of their loyal vassals to rebel out of fear for the most minor offenses that a less authoritarian government would let slide. Good examples include numerous cases in the Great Crusade where the Legions destroyed non-Chaos-corrupted human planets and their STCs (which the Imperium kind of needed), and in some cases those missions had direct Custodes-backed approval from the Emperor. A common theme in 40k is that the anti-Chaos races (Imperium, Eldar, Necrons, Tau) have really good reasons to put their differences aside and team up, but tragically cannot due to their own pride, ego, and dogma.
Similarly, the rigid class hierarchy the Imperium has produced has resulted in a large number of high-ranking Imperial military officers being closet-Khorne worshippers (demonstrated in books like Fire Caste), and a decent chunk of the Imperial nobles are worshipping Slaanesh in secret. The Imperium likes to claim that due to its indoctrination the "enlightened" individuals at the top of things can resist temptation and...they cannot.
This ties into a broader theme in the Warhammer multiverse: Chaos (the Immaterium) always wins. Fans don't like it because it reeks of nihlism, but this is the core theme of Warhammer that the authors and Games Workshop have repeatedly stressed in in interviews: Chaos will always win, despite being disorganized, because mortals are fundamentally self-destructive, self-advancing, combative, and can't leave well enough alone (which is seen by...the shape of the material realms in the various Warhammer universes).
But what all this means for your question is that it ultimately doesn't matter if a government is a liberal democracy or authoritarian theocracy, ultimately the Immaterium will destroy it and societal policies will do nothing to reduce how fast it comes. The pros and cons of a democratic versus an authoritarian government would come out in a wash, and ultimately the rates of immaterial incursion would be the same. A liberal democracy would have fewer people turning to Chaos, but would have a harder time catching Chaotic cults before they turned critical, and so the problem would be the same. It doesn't matter if you catch most of the Chaos cults, if you miss one your planet is doomed.
40k stories like to claim that authoritarianism is the only way to handle Chaos, but the stories are written from the biased perspective of indoctrinated Imperials raised from birth (or even brainwashed in the case of Astartes) to see no other way. This is shown by the large number of Crusade-era civilizations with better living standards than the Imperium and some knowledge of the dangers of the Warp that were able to survive just fine. The fact that the Imperium really can't tolerate an alternative, equally valid solution to their problems has been a core theme of 40k since day one.
Nor is this getting into the fact that the Immaterium has been shown it could win easily at any time, and the only reason the Imperium hasn't already fallen to Chaos is because 1) the Immaterium is sentient and likes the Imperium to be the hell-hole that it is, and 2) later 40k stories have played up the Emperor of Mankind as this deus ex machina that magically protects the society and gives humanity a win button from the consequences of dealing with the Immaterium. Unless your society has a 12 foot tall uber-psychic Hittite with gold armor running around you may need to find another solution.
The other, other thing to consider is that while no society could handle the Immaterium as seen in the present 40k timeline, it could probably handle the Immaterium prior to the War in Heaven. The "present" Immaterium is described as a maelstrom comprised mainly of the strongest and most harmful emotions known to rational beings. The Immaterium prior to the War in Heaven was a more nuanced place comparable to Avatar's Spirit World or the portrayal of the spirit world in a lot of animistic religions. Because the Immaterium then was less corruptive, less malicious, less aggressive, and you could actually reliably find good or neutral daemons and Warp entities, it would be easier to argue that a society (of any governmental structure) could handle such a dimension.