Q. Deuteronomy 21:15-17 talks about a polygamist who hates one wife and loves another as though this were an acceptable arrangement. This does not seem very inspired to me.
The translation is the problem here and has nothing to do with literal 'hating'. This is a Hebrew metaphor which Yah'shua (Jesus) also used to talk about different degrees of love:
Here the Saviour is simply saying that a disciple's love for Him must far exceed the familial love he has for father, mother, spouse, children or siblings so that in comparison it will seem as though he is hating them. This powerful imagery simply underlines the responsibility every believer has to the King and His Kingdom. Thus hating of one's own life is not a call to self-hate either but a call to put Christ first - nothing more, nothing less. Christ never taught anyone to hate a fellow human being. All we are permitted to hate is sin itself.
"If anyone comes to Me and does not hate his father and mother, his wife and children, his brothers and sisters - yes, even his own life - he cannot be My disciple" (Luke 14:25-27, NIV).
The same metaphor is used in Deuteronomy but in a different way. The issue is not 'loving' one wife and 'hating' the other but of putting one wife ahead of the other. A polygamist is supposed to love his wives equally as Christ loves us equally. But in the instance of a polygamist husband loving one wife more than the other, he is not permitted by the following Torah statute to disregard Yahweh's commandment as far as inheritance rights are concerned:
In other words, if he has two wives, and he loves his second wife more than his first, he is not allowed to give the double firstborn inheritance to the first son of his second wife, because the first son of the first wife has the responsibility to take care of family matters after his death, the double inheritance being given to ensure that all the needs of the wider patriarchal family are taken care of.
"When he wills his property to his sons, he must not give the rights of the firstborn to the son of the wife he loves in preference to his actual firstborn, the son of the wife he does not love [as much] ('hates'). He must acknowledge the son of his unloved wife as the firstborn by giving him a double share of all he has. That son is the first sign of his father's strength. The right of the firstborn belongs to him" (Deuteronomy 21:16-17, NIV).
All this Torah statute is doing is recognising reality, namely, that in the polygamous situation a husband who, because of his flesh, favours one wife over a another may be tempted to ignore this commandment concerning the economic rights and stewardship of the firstborn son. It isn't agreeing with the husband's partiality, it's simply warning him not to go changing the Torah willy-nilly based on his misguided passions.
So, no, I do not see any lack of inspiration in this passage. It demonstrates Yahweh's love in making sure the family is provided for in the correct way after the death of the husband. There is no licence here for a husband to hate one or more of his polygamous wives or to show fleshy favouritism.
 Family Idolatry: The New Covenant Salt Sermon