It is really hard when they are that age, because they want to be treated like adults when it suits them; but are quick to argue that they are a teenager and so will act accordingly.
It IS a really hard age, because they are adults in a physical sense, and transitioning children in an emotional sense. Teenagers are a pain in the bum because being a teenager is generally pretty shit. No parent always gets it right, especially when it comes to the teen years. But privacy is a pretty basic thing, and it is tied up with autonomy, respect and self.
I know it can be frustrating knowing there's a bomb site in the house, but ultimately it's private space. If it affects others - if they start leaving their mess in communal areas, or they're actually dirty and risk mould, smell or infestation, then yes, you have a right to take action if they really won't do it themselves. If it really is just as simple as 'I don't like the way they keep things in their personal space', then get over yourselves. As the song goes, your sons and your daughters are beyond your command. They're not you, they're themselves. If the worst you get in teenage rebellion is a messy room, you have won at parenting.
I am frankly appalled that anyone could be so scornful as to dismiss an adolescent's desire for private space as 'crap'. Not surprised, of course, because of the number of people who parent their teenagers based on point scoring and face saving, but still appalled. Imagine, at the difficult age of 15, being told that your private space could be invaded at any time because it's just 'growing woman crap'.
I do agree with PPs that when parents don't accept heir adolescent children's right to private space, it's because they still think of their children as extensions of themselves.