Hi, i agree with you but not sure he needs professional care about this. Start by having a talk with the boy and also the mother. You might threaten to call protective services if this continues.
I would explain that You are a modest household and value privacy, and that You expect Him to respect that, that You expect certain behaviors when He is in Your home. His maturity level should not be an issue as we teach modesty to our very young Children.
In answer to your title of the post, it is okay for the mother of your child to see him naked. I can't imagine that I'd ever see my child as anything but my child and therefore, seeing him naked wouldn't be the same as their friends being naked in front of me. In fact, if they had some kind of issue, it would be me or their dad that would check it out even if it were in an awkward place. ya know? It's my kid. always my kid. It's not sexual to see them naked.
Seeing me naked, well. some families are like this. At about the third grade level, my kids come into the room when I'm changing or showering and it is no big deal to either of us but they don't sit there and stare at me. I do put on a towel or a robe when they come in but not in a "oh my gosh, I'm naked, get out" kind of way. Just in a modest kind of way.
It's okay that some families are less modest.
So, I would not go down the path of saying there is something wrong with your ex wife and her rules or your son's complacency with them. I disagree with that and especially your 'new' wife's idea that he needs psychological or professional help.
BUT, it is okay to have your own rules in your house. You can tell him that it makes his wife and you uncomfortable so if he could please cover up and knock on the bathroom door (etc.), that would be great.
You've talked to your son about it. I think the necessary next step is to talk with his mother about it. Do you guys have a co-parenting relationship at all? How does she react when you bring up other issues to her?