I think there are two basic answers to your question. The first, and simple answer is:
- Many Protestant churches do not allow divorce. Some congregations deny membership rights to people who are divorced.
The more direct, and also more complex, answer to your question is:
Many protestant churches permit divorce because there is simply nothing they can do about it.
Divorce is a legal right in most places, regardless of whether the church allows it. Many Catholics get divorced, too. Although in the eyes of the Catholic church, such a divorce (and possible remarriage) is not recognized.
The consequences of divorce within the church are usually rather minimal. A divorced person cannot remarry in a Catholic ceremony, for instance. Many protestant churches and pastors will have similar restrictions, refusing to allow a ceremony of a divorced couple in their facilities, or refusing to officiate the ceremony for a divorced person.
However, beyond refusing to allow or officiate marriages, and possibly refusing membership rights to divorcees, there's very little any church can do to prevent divorce.
The same is true of practically any practice that is considered sinful in the eyes of the church. A church can only do so much in "discipline."
A second issue, beside the fact that churches are essentially powerless, is the concept of forgiveness.
Many churches are willing to forgive pass transgressions such as divorce, especially if they happened prior to conversion.
As Matthew 19:18 states,
Jesus replied, "Moses permitted you to divorce your wives because your hearts were hard. But it was not this way from the beginning.
Jesus is clearly pointing out that divorce is, in fact, legal. It is bad, but it is permissible. To turn it into an iron-clad law is then much like laws concerning the Sabbath - Jesus values the individual over the institution, even an institution as great as marriage.
(Note: Not advocating, just explaining the rationale!)
I think that the biggest issue is the exception in Matthew 5:32:
But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
The Catholic Church takes that phrase to mean, "except in the case of unlawfulness" (which is why there is an annulment process), but many take it as an "out." Regardless of the merit of such an interpretation, it seems that that "escape clause" has been used a bit more than it should be.