Is hate an abstract noun

Yes, hate is an abstract noun. An abstract noun is something that can't be experienced by any of the five senses; it can't be seen, heard, smelled, tasted, or touched. You may see the face of someone whose angry or hear the Words of anger, but the anger itself is what that person is feeling, not their face or their Words.

The Word hate is both a noun (hatred) and a verb (to hate).

Noun: Hate has a value when it spurs changes for the better.

Verb: Don't hate your enemy; succeed in spite of their hatred.