Polygamy - why does the Book of Mormon say its abominable but the church lived it?
The Standard of Marriage is Monogamy
The Church of Jesus Christ of Latter Day Saints Newsroom - Polygamy
The standard doctrine of the Church is monogamy, as it always has been, as indicated in the Book of Mormon (Jacob, chapter 2): “Wherefore, my brethren, hear me, and hearken to the word of the Lord: For there shall not any man among you have save it be one wife; and concubines he shall have none. … For if I will, saith the Lord of Hosts, raise up seed unto me, I will command my people; otherwise they shall hearken unto these things.”
In other words, the standard of the Lord’s people is monogamy unless the Lord reveals otherwise. Latter-day Saints believe the season the Church practiced polygamy was one of these exceptions.
Why then do individuals have polygamist marriages in the temple today. But the doctrine is only to have one wife?
The standard for God's Church today is Monogamy. That hasn't always been the standard. It has never stated that these marriages were temporary. In other words the marriages they entered into were not a temporary arrangement - they were eternal. Because they are eternal - it shows that the practice of polygamy is not temporal, or temporary but eternal.
The Nephites were not given the fullness of this doctrine - and were not allowed to practice polygamy. Jacob 2:24-29. To them - the practice of polygamy that David practiced was abominable to God. However, as we can see below they did not have the fullness of the doctrine. There was a clarification to this doctrine given to an authorized prophet at a later date to a different people see D&C 132:38-39 wherein this was clarified. In that David received these wives from Nathan God's servant and in nothing did he commit sin except when he went beyond what God commanded. Thus our understanding of the doctrine of Polygamy was clarified and greater light and knowledge was given on the subject.
The greater understanding of this doctrine is that a man can have more than one wife without that being abominable to God. There may be additional revelation clarifying even more, but until then our doctrine is based upon the scriptures. So... that is how it is.
Based upon this a man currently can have more than one temple marriage if his wife dies or what have you - because that is the doctrine as we understand it now. They will be his wives in the next life. The church itself does not perform these ordinances for the living - because Monogamy is the current Standard - but Polygamy is the doctrine based upon the scriptures.
30 For behold, thus saith the Lord God: I will give unto the children of men line upon line, precept upon precept, here a little and there a little; and blessed are those who hearken unto my precepts, and lend an ear unto my counsel, for they shall learn wisdom; for unto him that receiveth I will give more; and from them that shall say, We have enough, from them shall be taken away even that which they have.
This is not a contradiction - it is a clarification of the doctrine. Our understanding of doctrine is not even now complete and we expect it to change over time as I stated above.
For an even clearer explanation of this issue see the link below with examples and links.
This is one of the great things about this church - our knowledge is constantly increasing, our understanding is growing, and we have a prophet who today can tell us God's will for us to live by today!