What with the horrible fate they inflict upon innocent sentient life forms and all. If your survival means that you have to kill lots of innocent people (and the denizens, as stated above, do far worse than that to their victims), then you ought not exist from a moral standpoint. Great Freudian Excuse and all, but it still doesn't change the fact that they are all in dire need of a headshot, preferably severalof them.
Although it could be said that they are a higher form of life, when compared to humans, we are but food. Nothing more, nothing less.
By that logic, it is okay to root for a shark if it manages to eat a family member or friend in front of you. They are but food. Nothing more, nothing less.
You don't have to "root" for the shark, or the common house cat for that matter. You simply have to understand that killing is not inherently evil. Hunting to eat is what animals do. Even herbivores cause the death of insects when they eat.
By the opposing logic, you could argue that humans are just as bad as Denizens if you consider killing for survival to be evil. In order to eat, we slaughter plenty of animals on even a daily basis. Depending on how far you're willing to stretch it, even vegetarians and the like benefit from murder; ripping parts off living plants or devouring their unborn children (seeds). Is this fine because we're "higher" than plants and other animals? If so, then us getting devoured should be fine too; we're just lower on the food chain than we'd like. If it's not okay, then we still don't have the moral high ground and ought to be killed off for being monsters in our own right.
Opposing said opposition, humans may kill animals to eat to survive, but humans are also against unneeded cruelty against animals and outright forbid killing and eating other sapient beings. Crimson Denizens, on the other hand, know that humans are sentient just like them, but they still proceed to be unnecessarily cruel to them, and don't care about searching for other alternatives. Killing to eat to survive in one thing, being cruel and downright malicious to those you feed on is a different story.
Difficult to root for the Denizens with examples like Friagne, the Twins, and Annaburg. They are higher only in the sense of being able to use power of existence. Yuji all by himself shows that they're no more intelligent. Tenmoku Ikuo has shown that humans that sacrifice their humanity and live consuming Denizens can also be quite powerful, although it's true that according to the anime he's actually three entities including the sword.
Attitudes of Flame Hazes
Given that the general attitude of Flame Hazes towards humans ranges from indifference to contempt, this one had a difficult time sympathizing with their cause. Now in the third season we see Tomogara eating, drinking and displaying rather human characteristics, the actions of the Flame Haze in the latter half of the season, especially The Four Gods of the Motherland could be characterized as genocide of a sentient species.
Another point to not Rooting for the Empire is that Flame Haze went to war on the Crimson Denizens because they would have eaten large amount of human existence in short amount of time that would cause The Endofthe Worldas Weknowit if left uncheck. The Snake of the Festivals offer them a world where they could feed on human without any consequence. The Crimson Denizens are like greedy jerks like CEO that make large bonus for themselves or farmer using the land every year not caring if the company or land is ruin as long they make a profit now.
It should be noted that Yuji's original plan was to create a copy of the world, but Shana made rule that the Crimson Denizens can no longer eat humans in the new world which they agree to.
It would be possible to devour humans but they didn't need to do it to survive. Shana and the other Flame Haze didn't believe the Crimson Denizens could resist the temptation even when they no longer need to do it to survive.