Chewing of the cud isn't really important. The divded hoof however can be. Here is how:
Leviticus 11:6King James Version (KJV)
6 And the hare, because he cheweth the cud, but divideth not the hoof; he is unclean unto you.
NOTE: "DIVIDETH not the HOOF"
Is a contridiction on its own, why? For the FACT that rabbits do NOT HAVE HOOFS. So how can they not have "divideth not the hoof" when they do not even have hoof. See what i mean.
Rabbits have PAWs:

NOT
HOOF:

Or cloven Hoof:

This same goes for Rock Badger, this it is an error in OT that indicating rabbits for not dividing the hoof, when in truth they DO NOT even have hoofs thus, they shouldn't even have been mentioned with such criteria.
Quran mentions that allah swt prohibites the jews:
Quran[6:146] "And to those who are Jews We prohibited every animal of uncloven hoof; and of the cattle and the sheep We prohibited to them their fat, except what adheres to their backs or the entrails or what is joined with bone. [By] that We repaid them for their injustice. And indeed, We are truthful."
There are certain things that Prophet Isreal prohibited to himself:
[3.93] All food was lawful to the children of Israel except that which Israel had forbidden to himself, before the Taurat was revealed. Say: Bring then the Taurat and read it, if you are truthful.
So what have we learnt.
1. Rabbits do not have hooves thus cannot divideth the hooves. Thus meaning this criteria isn't sufficient to classify them.
2. Quran tells us muslims what is forbidden to us and what is forbidden to jews. Thus meaning what is forbidden to jews is not all the same is what is forbidden to us muslims because, allah swt gave them such strict rules as punishment for being continous transgressors.
3. All was lawful to jews before Torah except what Isreal forbidden himself. Meaning "Chewing of Cud" and other animals that do not match up with Quran(6:146) are insertions. This meaning it is a cultural practice that they inhereted from prophet Isreal.
4. Prophet Muhammad pbuh did not break the commanded of Torah, why? 1. What was revealed to him that allah swt prohibited the jews did not include camels and rabbits. 2. What was revealed to prophet muhammad pbuh is that jews and muslims have similar but different dietry restrictions from allah swt. 3. Since prophet muhammad pbuh never stated that i came to follow the Torah and Injeel, thus Torah and Injeel are irrelevant to prophet muhammad pbuh.
Why?
Simple because Quran is law for prophet muhammad pbuh and muslims and Quran supercedes what came before it:
Quran[2:106] "We do not abrogate a verse or cause it to be forgotten except that We bring forth [one] better than it or similar to it. Do you not know that Allah is over all things competent?"
Chewing of the cud isn't relevent since quran makes no mention of it being enforced by allah swt onto them.
Allah swt knows best. =)