Early church leaders could do little in practice, though as a rule they strongly opposed second marriages for any reason. Saints Paul, Augustine, and John Chrysostom all frowned on remarriage, but allowed it if it followed widowhood* rather than divorce, imposing penalties on those who did marry a second time. They all agreed that a priest could not marry more than once. Church councils affirmed the right to remarry after the death of a spouse and most did not forbid it after divorce. They could hardly have done otherwise. The practice was common enough, having previously been completely legal, that forbidding it would have no practical result. This remained the case throughout most of the Early Middle Ages. Remarriage after widowhood was allowed but discouraged. Divorce with remarriage was equally discouraged, but common. A person whose spouse disappeared had to wait a certain period of time before they remarried.**
Reformers in the 11th and 12th centuries, however, promoted the idea that marriage was an unbreakable bond. They opposed the remarriage of widow(er)s, but took an even stronger stance on divorce. A marriage could only be ended by the death of a spouse. Couples wishing to end their union could get either a separation (which meant they were still married) or an annulment (a declaration that marriage had never been valid in the first place***). Only an annulment came with the right to remarry. This was the ideal. It did not yet have the force of practice.
By the 13th and 14th centuries there was little to no opposition to the remarriage of widow(er)s, though some Church leaders regarded second marriages as spiritually incomplete. The opposition to divorce, however, had become a crackdown. Cases among the lower classes, who in many places continued to engage in clandestine marriage, often only came to light when they came to court, but the middle and upper classes faced more scrutiny. This would become a significant issue in the Reformation, with reformers and Protestants generally arguing in favor of remarriage after divorce, and Catholics opposing divorce on principle. Nobody opposed the remarriage of widows.
*For simplicity’s sake, when I say “widowhood” I am referring to both men and women. For most of this time period, the law made little (but not no) difference regarding gender when it came to the remarriage of people who had lost their spouses.
**Church leaders never did agree on how long that period should be.
***As a result of, for example, a defect in consent.