There are three questions:
Question 1 the title says
Does God love those who love him and hate those who hate him?
The passage does not say that God hates. The passage says that God destroys those who hate him. God loves everyone and even though no one deserves it God has provided a path to forgiveness.
6 You see, at just the right time, when we were still powerless, Christ died for the ungodly. 7 Very rarely will anyone die for a righteous person, though for a good person someone might possibly dare to die. 8 But God demonstrates his own love for us in this: While we were still sinners, Christ died for us.
9 Since we have now been justified by his blood, how much more shall we be saved from God’s wrath through him! 10 For if, while we were God’s enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life! 11 Not only is this so, but we also boast in God through our Lord Jesus Christ, through whom we have now received reconciliation.
These verses seem to say that God will love those who love him and repay with evil/destroy those who hate him. Is that generally true of God in the Bible?
If by "generally true" you mean a truth that is sometimes asserted or roughly asserted or sort of an on average statement then no, it is not generally true that God will love those who love him and destroy those who hate him.
In the Bible it is an absolute truth and a key truth in Scripture.
It seems to be a theme throughout the Old Testament; does it change in the New?
No, it does not change in the New Testament. Michael16 has done a nice job of sampling passages in the Old and New Testaments that demonstrate consistency between the Testaments.
From another perspective, thinking of the message of the New Testament, one of the key points of Jesus life, death, and resurrection is that God is providing salvation for those who are in rebellion against God.
Let's look at the larger passage.
1 When the Lord your God brings you into the land you are entering to possess and drives out before you many nations—the Hittites, Girgashites, Amorites, Canaanites, Perizzites, Hivites and Jebusites, seven nations larger and stronger than you— 2 and when the Lord your God has delivered them over to you and you have defeated them, then you must destroy them totally. Make no treaty with them, and show them no mercy. 3 Do not intermarry with them. Do not give your daughters to their sons or take their daughters for your sons, 4 for they will turn your children away from following me to serve other gods, and the Lord’s anger will burn against you and will quickly destroy you. 5 This is what you are to do to them: Break down their altars, smash their sacred stones, cut down their Asherah poles and burn their idols in the fire. 6 For you are a people holy to the Lord your God. The Lord your God has chosen you out of all the peoples on the face of the earth to be his people, his treasured possession.
7 The Lord did not set his affection on you and choose you because you were more numerous than other peoples, for you were the fewest of all peoples. 8 But it was because the Lord loved you and kept the oath he swore to your ancestors that he brought you out with a mighty hand and redeemed you from the land of slavery, from the power of Pharaoh king of Egypt. 9 Know therefore that the Lord your God is God; he is the faithful God, keeping his covenant of love to a thousand generations of those who love him and keep his commandments. 10 But
those who hate him he will repay to their face by destruction;
he will not be slow to repay to their face those who hate him.
11 Therefore, take care to follow the commands, decrees and laws I give you today.
What is going on here?
God has established a special relationship with the Israelites and is giving instructions for how they should behave in the land God will give to them.
Two paths are laid out:
- Enter the land and do not integrate in any way with the existing inhabitants of the land. Instead, be faithful in their covenant relationship with God. Verses 1 - 9
- Demonstrate open rebellion, hatred toward God, scorn God's grace and refuse to acknowledge God's sovereignty over them by adopting false gods. Verses 10 - 11
The Israelites could choose faithfulness or they could choose their own destruction.
We have a similar choice today.