Legal Question in Family Law in Texas

It could be, depending on how the person knew the spouse's password. If the person stole the password, there could be a problem. If the spouse freely shared the password OR saved his or her password on a shared computer, the conduct is probably fine.

In a sense it doesn't matter: If it is illegal, what is the likelihood that the police are going to investigate the "crime" and then the District Attorney is going to decide to prosecute and then the Grand Jury is going to indict and then the judge is going to send someone to jail over this? None of that is going to happen, so in a sense, who really cares what the criminal law has to say in that matter?

Just to be safe, the spouse who allegedly logged in should immediately send the other spouse a spoliation letter and discovery requests demanding the full history of the other spouse's Facebook activity. The court will order the incriminated spouse to turn the information over and plenty of case law shows that a person who deletes their FB history is VERY LIKELY to go to jail if that FB history was responsive to a discovery request.

Why go grab what you can force a person to turn over to you?