Death is not worse pain than an empty life. -- Lun Tha

Can the God who made Heaven and Earth hate?  Can God, who allowed his own innocent son to pay a bloodguilt debt for all mankind because he loved us so much...hate?

Yes.

He doesn't hate people. He hates what we do.  Please understand that.  He is GOD and he has standards and those standards are not nebulous. They are clearly stated.

arrogant eyes -- someone who sees others as inferior
lying tongue -- obviously, someone who spreads untruths on purpose
hands that shed innocent blood -- the key word here, I believe, is innocent
a heart that plots wicked schemes -- this is not even enacting the schemes...but just plotting them, taking the time to mull them over, to perhaps enjoy vengeful or disruptive thoughts... that is what the Lord hates
feet eager to run to evil -- ever felt that morbid curiosity to see what is "wrong?" Also those who are eager to find what is wrong, what is "not good."
a lying witness -- someone who, when asked, will lie about something or someone else. Often, this means for the advantage of the liar or the disadvantage of whoever or whatever is being testified against. Implies for a falsely-gained benefit for someone.
one who stirs up trouble among brothers -- someone who agitates brothers/friends/companions/a unified group.  This does not imply that telling the truth to people is agitation of brothers. What this is speaking to is that God hates that which causes dissension for the sake of dissension among people who are otherwise unified.

You will perhaps notice, that the first six things are not people so much as their actions.  "A lying witness" is a person, yes, but a person in a specific role.  God hates the act of a person who is lying. The last is something that the Lord detests.  That he finds despicable and that he doesn't want around him. 

Nowhere here does it say that God hates any specific group.  God's hatred in this passage is reserved for actions.

His love, though, he extends to people. And though he hates our actions, many times, he loves us dearly and will forgive us and cast our hated and detestable acts far from him, leaving us, his children, to feel the relief of reprieve.