Religions don't cause wars, people do.... religion is an excuse at best.
Every Abrahamic religion forbids murder - the Muslims have jihad as special get out clause - but there is no such exception for Jews or Christians. you can't have a war motivated by Judaism, even if Israeli soldiers kill more Palestinian children than Israelis have been killed by Palestinians... thats not religion - its politics and evil.
I don't see any Buddhist, Shinto or Sikh spawned wars in our history books either... maybe I don't know enough but I feel that the 'religious war' is a phenomenon that could even be exclusive to the Abrahamic religions...
Not a very easy question to answer. Religions apply the love aspect to their in-group, I think, and members can narrowly or broadly define that group. The societies that religious leaders deem as heretical are unworthy or too misguided to deserve love from their god. As an extreme example, during the Inquisitions, religious leaders branded people as witches, and witches were undeserving of mercy or pity. They play semantic games. Although, that's just one reason.
I think there's many different reasons why people hate.
Also, the larger a religion gets, the more denominations or splinter groups you're likely to have, and each splinter group may interpret their religion's doctrine differently. We hear about the violent splinter groups because the peaceful ones don't stick out. And then different splinter groups go pointing fingers at each other, crying, "You're not true Christians/Muslims/Jews... whatever.
It's a complicated mess.
And then there's the fact that the members are all just people, good and petty people all around, interpreting their doctrine to suit their agenda.
I'm sure there are other reasons.