Leave it alone and stay out of your parents' personal marital life. I'm sure that, if he has a profile on Ashley Madison, both your parents know there is a problem within the marriage. They will fix it if that's what they want to do, otherwise they will continue living as practical strangers.
Yes, your father's behaviors has impacted you and you don't like it, i can't blame you.
Adult relationships can seem complex, and when we have never been married, do not understand the dynamics of a marriage which isn't that great, we WILL feel upset, especially if they are close with us, and family.
Still, their marriage is between them, not yours to manage.
If you are going to mention this to anyone, you can casually let your father know you have seen his profile. It might not be a great idea, but if you can't contain yourself, then approach him when the two of you are alone.