Your Bible questions are:
>>can a man and woman divorce for any reason and be all right so long as neither has sex with any else for the rest of their life? If a couple divorce for irreconcilable differences is either party free to remarry as soon as the other commits fornication?<<
The basic teaching of scripture from the beginning of time regarding marriage has been (and is): One man and one woman for life (read Gen. 2:21-24; Matt. 19:3-6; Rom. 7:2-3; 1 Cor. 7:39).
Jesus gave one exception for legitimate divorce and remarriage to one party within the marriage: that cause is fornication (sexual immorality). Jesus gives the person who divorces his or her mate for the cause of fornication the right to remarry (read Matt. 19:9; 5:32). When divorce occurs for any other reason, and remarriage follows, adultery occurs. Also, it is clear that the adulterer is not free to remarry with Christ's approval from Matthew 19:9.
God hates divorce (Mal. 2:16). Men and women are to honor marriage and not put asunder what God joins together (Heb. 13:4; Matt. 19:6). Therefore, to put asunder a marriage that God has joined together is sin. If one violates his (or her) marriage vow by committing fornication, the innocent person has God's approval to put away the fornicator and remarry (Matt. 19:9). God does not give any right of remarriage to the fornicator or to people who are divorced for any other reasons. Such are to "remain unmarried or be reconciled" (1 Cor. 7:10-11).
With these Biblical truths before us we can now answer your specific questions:
>>can a man and woman divorce for any reason and be all right so long as neither has sex with any else for the rest of their life?<<
No, it is not "all right" to divorce "for any reason", for God hates divorce (Matt. 19:6; Heb.
13:4; Mal. 2:16). Nor should that sin be compounded by unlawful
remarriages. 1 Corinthians 7:10-11 teaches that those who are divorced (excluding
the exception of Matthew 19:9) are to remain
unmarried (which would mean no sexual relations with anyone else)
or be reconciled.
>> If a couple divorce for irreconcilable differences is either party free to remarry as soon as the other commits fornication?<<
No, Matthew 19:9 says that if their divorce was not for the cause of fornication their remarriages are adultery.
Matthew 19:10-12 teaches the sacrifice of faith to pay the price of faithfulness to God. In many cases that means celibacy. But, heaven will be worth it all! (Col. 3:1-4)
I hope this helps. The Bible Answers website at www.bibleanswer.com has additional material on marriage, divorce and remarriage (look under "Special Studies").
God bless you as you study and live His word.
Joe R Price
Mt. Baker church of Christ