In the setting there are humanoid animals and the biggest problem is the instinct of the carnivores as predators. But in the real world the thing that makes the humans the dominating species is their intelligence, mostly because they can make stuff, like guns for example, and animals don't have any chance against guns. The characters also have intelligence and guns, and any other kind of weapons too, so why is the carnivore vs herbivore such a big matter?
I viewed the carnivore vs herbivore as a form of racism in the Beastars universe, as there is even racism against interspecies couples.
Because the carnivores are so different (They have to eat animal based protein to survive, they have built in weaponry [fangs/claws/beaks], are almost always physically stronger and physically imposing, some can see in the dark) these differences are enough to create tension between them and herbivores.
Pair this with the various killings that always appear to be carnivores preying herbivores, and the fact that there is an illegal market to buy meat and herbivore parts, and now you have a larger problem with how herbivores view carnivores.
It is also extremely likely that the Beastars Universe does not make Guns an "Equalizer" because of gun culture in Japan. Japan makes gun ownership a rigorous process and citizens are essentially encouraged not to own a gun in Japan.
If Japanese people want to own a gun, they must attend an all-day class, pass a written test, and achieve at least 95% accuracy during a shooting-range test. Then they have to pass a mental-health evaluation, which takes place at a hospital, and pass a background check, in which the government digs into their criminal record and interviews friends and family. They can only buy shotguns and air rifles — no handguns — and every three years they must retake the class and initial exam.
[...] Each prefecture — which ranges in size from half a million people to 12 million, in Tokyo — can operate a maximum of three gun shops; new magazines can only be purchased by trading in empty ones; and when gun owners die, their relatives must surrender the deceased member's firearms.
[...] Off-duty police aren't allowed to carry firearms, and most encounters with suspects involve some combination of martial arts or striking weapons. When Japanese attacks do turn deadly, they generally involve fatal stabbings.
So because most citizens are not encouraged to have guns, the next designation of power is the aformentioned "built in weaponry" of the carnivores.
The other thing to remember is that so far (in the anime series) we've only seen shady groups that were in power or had power (The Shishi Gumi, or equivalent of the Yakuza or mob) have guns. None of the other animals that were "upstanding citizens" were shown having a gun, with the exception of Rouis when he stole a gun from one of the Shishi Gumi members and used it to attack. This probably means that they got their guns through a black market and are not documented as having any even though everyone knows the mob owns guns.