Students at the school said the two were often at odds with each other. As a teacher, you have to make it very clear to students who make it clear that they do not like each other that acting on their feelings is unacceptable in school. You may need the help of parents or of your school's administration. This is different from group hatred. You as a teacher are probably incredibly tuned in.
Most teachers are.
If you sense a dangerous rivalry, bring in the parents and administrative personnel right away. Be firm that this kind of tension and anger will not be accepted in your classroom. You need to trust your gut feelings. I'd go straight to the principal and maybe others, like child-abuse professionals or the police. Teachers, like kids, don't want to rat on kids or be seen as weak because they can't handle particular kids.