I would say since it is not at all a marriage in God's eyes but fornication...
This is the key premise. Is it valid?
This view comes from a particular interpretation of the teaching of Jesus in the Gospels.
This is one of the relevant passages from Matthew 5:31-32
[Jesus taught,]"
It was said, 'Anyone who divorces his wife must give her a divorce certificate,' But I tell you that everyone who divorces his wife for any reason except sexual unfaithfulness makes her the victim of adultery, and anyone who marries a divorced woman himself commits adultery."
Jesus is teaching in a very specific cultural context, but the truths can be extracted from it.
In this culture, women were not allowed to initiate divorce in any standard way. Moreover, if they found themselves divorced, they were in a terrible social and economic position and would have to turns to relatives or the kindness/malevolence of strangers to make their way in the world. Moses has allowed men to give women a certificate of divorce as a small grace to women so they could avoid being executed for adultery or facing endless abuse by a husband who wishes he were not married to her anymore. I can't help but think that Moses expected that allowance to be used sparely, only by the more hard-hearted men, but it was apparently much more common than it should have been in the days of Jesus. There are some commentators who believe that since execution was strongly discouraged under Roman occupation, certificates of divorce were used in place of execution to justly end a marriage destroyed by adultery.
A woman released under a certificate of divorce was under a cloud of suspicion as an adulteress, no matter what the real cause. If a woman tried to get her life together and found a new husband, the new husband would have to enter into the previously divorce woman's shame, thus also stained with the social and religious stigma of adultery - regardless of the truth of the situation.
We need to notice a couple of things:
1.) Jesus does not claim that the new marriage is invalid. He could have easily said that, but he didn't. He mentioned it in terms of the marriage bond.
2.) The command is pointed toward men, not women.
3.) I am convinced Jesus is condemning a social practice of the Jewish community where they weer almost casually mistreating women and justifying it in terms of being religiously correct (that is, the certificate of divorce authorized by Moses). That fits with the context of the "You have heard, but I say" passage. Jesus goes on to describe the stigma that follows from that unrighteous act.
The stigma of being divorced - even when it is scripturally justifiable - is a real thing. For example, things in American Christian culture have changed now, but back in the 1960s-1970s, divorced people were treated with great suspicion in Christian circles. I know this because I lived through that era and heard the gossip and saw the second wave of devastation as even those who were legitimately divorced faced open contempt from church folk.
Even when I ultimately divorced by first wife in the mid-1990s because of continual infidelity and finally abandonment over the course of two years, I took a LOT of grief from well-intentioned but completely clueless people who made grand assumptions about who was at fault and the motivations I allegedly had for finally taking steps to legally end the marriage (the marriage had been over in reality for nearly a year). "Spiritual" people assuring me that I was at fault and I had a girlfriend waiting in the wings, which was completely untrue. I also had several tell me that "my type" (whatever that is supposed to mean) would hop from woman to woman for my own sexual gratification, and that they would be proven right because I would be remarried within a year. In reality, I wanted nothing to do with marriage (or most church people like that) for quite a few years. I eventually "rushed" into another marriage 11 years later and have been quite happily married ever since.
