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In most cases, the church recognizes that they should acknowledge their past sin and resolve to be faithful from now on to one another. Why is this the case? It's because their marriages may have been sinfully entered into, but they are, in fact, marriages.

That's a different doctrine from what is found in the Scriptures. In fact, the author should realize this, since he referred earlier to John the Baptist's condemnation of Herod's adulterous marriage.

"For Herod himself had sent forth and laid hold upon John, and bound him in prison for the sake of Herodias, his brother Philip's wife; for he had married her. For John said unto Herod, It is not lawful for thee to have thy brother's wife." - Mark 6:17-18

Do they repent of this adultery by doing the same sinful action again, abandoning and divorcing one another?

John didn't say, "It wasn't lawful for you to marry her...But since you're married, it's all good. You certainly don't want to sin again by divorcing her."

John didn't say that to Herod. No, that's MAN'S surrender to the evil of divorce and adultery. GOD, through John, said, "It is not lawful for you to have her."

Sorry Lears that’s under the law of Moses(Leviticus 20:21). As a Christian we are not under the law, but under the Grace of God. There are other arguments, but that’s not one of them.