What would make the evidence relevant?
"It's often relevant, but in ways people might not expect. Most states have adopted a sort of 'no-fault' perspective to divorce. As a result, most states don't punish people in terms of property division or maintenance for marital misconduct. But, courts in virtually all states are willing to consider martial misconduct when it involves a misuse or dissipation of the party's assets -- so to the extent that any money has been used to pursue this relationship... courts will be interested."
Martial misconduct is also relevant when it comes to custody battles, "to the extent that it shows that somebody's lifestyle, or their habits, or the people that they have in their home would not be wholesome for the safety of the child and would affect the best interest of the child -- then it's relevant, and it's testimony that the court should and would hear.
How embarrassing is this going to get?
"So in cases like that, at a minimum, it becomes very embarrassing for the party -- the discovery of something like Ashley Madison would tend to stimulate a number of questions." Cordell also says that the other party may send out subpoenas if they know who their spouse cheated on them with, and they may bring that person in for a deposition.