This is a very important question that needs to be fully debated. I believe there are better answers than this question.
Answers provided do not address the history of this human behavior. Why did God find it right to give his children (men) such as King David, etc, more wives? Why did God allow Abraham to have a child from another woman when He knew Sara would still provide him with one? Why do Muslims have more than one wife?
I also tend to think that there is some chemical composition in men as compared to women that influence this type of behavior in some men.
I noticed that noticed that most of the contributions to this important (Why do women accept married men?) came from women and infact “married women” who, expectedly, would give same opinions which are not balanced enough to fully provide a clear understanding of this human behavior.
In my view, we also need contributions from those who have studied human science, women who have been involved with married men, married men who have been involved in another fixed relation for short and long time, men and women in polygamy marriages, etc.
I was grew up with a strong Christian belief of having only one woman in my life and when I got into my first relationship, I have my wife all my life because I believed we were one. There was no decision or action I made in my life that my wife did not know but what I always ended up getting was very opposite hence we parted peacefully. The same happened with my second relationship. Advices I get from men who have maintained their first marriages is that I give too much focus on one woman to the extent that they get too used, stop to appreciate and start to abuse your nature.
I suggest that you get well rounded views to this question which I think can be helpful to those who don’t fully take care of their marriages because they believe once they are married the hard work of nurturing the marriage is over because the partner is now locked up tome and me alone.