Why does the Lord seem to be lenient with polygamy in the Old Testament? It seems that the Old Testament is full of specific instructions with the exception of polygamy as if the Lord was “ok” with it.
The first thing to notice is the difference, as noted in the question, between being “lenient” and being “‘ok’ with it.” There is sufficient Scripture in the Old Testament to show that God’s intent was for a man to have one wife. In the New Testament, this is explicitly stated as a requirement for elders (“overseers”) and ministers or deacons (1 Tim. 3:2, 12). Yet, in the Old Testament, many prominent servants of God had multiple wives; David and Solomon are notable examples.
Examining the issue of divorce sheds light on this issue. In Matthew 19:7–8, we read, “They [the Pharisees] said to him [Jesus], ‘Why then did Moses command one to give a certificate of divorce and to send her away?’ He said to them, ‘Because of your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so.’” The important phrase here is “Because of the hardness of heart.” So, as stated in the question Jehovah was really being “lenient.” with his followers in view of their weakness (Ps. 103:14).
As in the case of divorce, “from the beginning it was not so.” When God created Adam He gave him one wife. That is the pattern “from the beginning.” In addition, there are warnings even in the Old Testament against “multiplying wives.” This caution was especially directed toward the king (Deut. 17:17). And, here the reason given was “lest his heart turn away.” This certainly happened in a notorious way with Solomon (1 Ki. 11:3-4).
There are also hints given in the lives of others where there is no explicit prohibition. In the opening chapters of 1 Samuel we learn of Elkanah who had as wives Hannah and Penninah. First Samuel 1:6 suggests that Penninah caused Hannah real grief, probably harassing her because she was barren. So, it is quite easy to see that strife and family difficulties would result in such a case.
In the New Testament, marriage is given as a picture of the union of Christ with His Church (Eph 5:32). So, the matter of polygamy and divorce takes on a far more serious significance. Today with the help of the Spirit of God there is less excuse for divorce and even general society still resists polygamy. Sadly, we must recognize that even among Christians divorce is sometimes unavoidable. No individual, no matter how devoted to the Lord, can force their spouse to act in a particular way. In the end, we need to trust God’s mercy to prevail.