Sure.

Your statement is that some people hate others because they want to restrict Muslim immigration.

One group says either there is no risk or the risk of terrorism is acceptable, the other disagrees.

Both cannot be correct at the same time, therefore one is lying.

I could stop there, having proven that the cause of hatred is based on a lie. Heck, that's more thought than most people apply to their hatred. But if we want to eliminate the hatred we need to ask why again.

Perhaps it is unwise to accept refugees from the nations we oppress and otherwise cause trouble in. I doubt that accepting refugees makes the oppression any more palatable. Perhaps if our armies left their lands and we stopped interfering with their self governance, there would be no terrorism. What else will accomplish that? 

That would eliminate the hatred described in your initial statement.