Hi,
I would allow everything honestly. No build is 'broken'. Some don't really make sense though...
don't make sense *to you*
Judgmental much?
Paladin 5/Warlock 3 for extra spell slots and non-stop smiting. His deity would abandon him if he sold his soul for power...
Except for the deities that don't care, and except for all the pacts that don't involve selling a soul, and except for all the exceptions. Like: Paladin of good deity is offered power by a fiendish entity whose only condition is that the paladin use that power to kill stuff, confident that even if the paladin starts off good, power will corrupt. Meanwhile, the good deity doesn't care at all, as long as the paladin kills the right stuff, and will even reward the paladin more in the afterlife for resisting more temptations.
Moon Druid X/Monk 1 for the AC boost. Kung Fu Panda isn't a thing...
Except, of course, for any game in which kung fu panda *is* a thing. All that's missing are stats for a panda. Besides, a real powergamer will prefer a kung fu bear or wolf or dinosaur. My kung fu is so strong that rather than just imitate a bear, I can *be* the bear.
Lore Bard X/Life Cleric 1 for the heal boost. "I tried religion once... Not my thing. Learned some tricks though." Come the f*ck on
Come the f*ck on indeed: I'm mostly a pop singer, but I study a little Kabballah on the side because I'm a really spiritual person. I'm a singer/songwriter who died recently, but in life I retreated to a Zen monastery for a few years and then returned to singing. Nope, no one like that in real life. Totally unrealistic. "I'm mostly a bard but pay my dues to the Lord of Song." "I started to become a priest but the Grand Poobah said that I will reach more people through my music, and that the gods gave me my mad skillz for a reason."
At the end of the day, it's just a game. We all play for different reasons. Some people care more about powergaming than character background (this is the optimization forum afterall). Who's to say what we should find fun? Let your players make the characters they want to play. As DM/God, you have the power to balance things in your game via other means.
By the way, none of these proposed power builds are overpowered. Of course, if you don't like them, you don't need to justify your preference. Anyway, Ken