How can hatred be for the sake of Allah and love for the sake of Allah, and does compassion for a disbeliever and wishing for their guidance contradict hating them for the sake of Allah? What is the ruling on naturally loving a close disbeliever? And how do we understand Allah's love for His awliya' (saints/devout servants), and is it similar to the love of His servants?

Hatred for the sake of Allah means hating a person because they disobey Allah’s command, while love for the sake of Allah means loving them because they comply with Allah’s command. Pitying a disbeliever and wishing for their guidance does not contradict hating them for the sake of Allah. Natural love does not contradict hatred for the sake of Allah, just as one loves medicine for its benefit while disliking its bitterness, or loving a unjust Muslim for their faith while disliking their injustice. The attribute of love for Allah Almighty must be affirmed in a manner befitting Him, without delving into its how, just like all His other attributes. The Ahl al-Sunnah wa al-Jama’ah affirm for Allah whatever He has described Himself with or what His Messenger has described Him with, without distortion, denial, anthropomorphism, or resemblance. Allah’s assistance to His allies is among the fruits of His love for them, and not the love itself. The Lord’s love for His allies is an attribute in addition to His mercy, benevolence, and giving, for these are the effects and requirements of love. All evidence points to affirming the servant’s love for their Lord and the Lord’s love for His servant. Affirming love and other attributes for Allah Almighty in a manner befitting Him does not involve anthropomorphism. Nu'aym ibn Hammad al-Khuza'i said: "Whoever likens Allah to His creation has disbelieved, and whoever denies what Allah has described Himself with has disbelieved. There is no resemblance in what Allah has described Himself with or what His Messenger has described Him with. So, whoever affirms what the clear narrations and sound reports have conveyed in a manner befitting His Majesty, and negates imperfections from Allah, has indeed followed the path of guidance."