In one sense this is true. There is a movement afoot to claim that it’s okay to pray doom and destruction on our enemies because King David did so. This is false. Jesus superseded the OT morality, especially when it comes to enemies:
Matthew 5:43-48
“You have heard that it was said, ‘You shall love your neighbor and hate your enemy.’ But I say to you, love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven; for He causes His sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous. ...
I don’t believe the OT ever told anyone to hate their enemy. Do you have a passage in mind? Jesus doesn’t say it did in the passage you quote. He’s merely quoting a misunderstanding of the OT law before correcting it.
In fact, in Ex. 23.4-5, Moses said: If you meet your enemy’s ox or his donkey wandering away, you shall surely return it to him. If you see the donkey of one who hates you lying helpless under its load, you shall refrain from leaving it to him, you shall surely release it with him.
In Lev. 19.18, Moses said: You shall not take vengeance, nor bear any grudge against the sons of your people, but you shall love your neighbor as yourself; I am the Lord.
Jesus teaching what we call the golden rule was a quotation from Lev. 19.18, not superceding the OT.