Sometimes, you want the world to watch you play games. Sometimes you want to just play alone. And those times, it seems like no sooner than you get into the main screen of your favorite game, boom: here come the invites, messages, and all the other stuff you don't want to deal with. You just want to game in peace!
Fortunately, you can easily hide your online status on the PlayStation 4 and Pro so you can game without being bothered. Here's how to do it.
From the PlayStation's main screen, scroll over to the Profile icon. This is found in the "options row"---the one just above the list of installed games and apps.
The top option on your profile, found just below your profile picture, reads "Set Online Status." This is what you're looking for.
There are two simple options here: "online" and "appear offline." You want the latter, of course. When you select it, a warning will show up letting you know that other players may still see you as online in certain games/situations. This only shows up once, though.
That's pretty much all there is to it. The little blue icon beside your profile picture will turn to a small red X, letting you know you're basically invisible---this will also show up in the options bar.
Lastly, you remain offline until you set yourself back online, so it's worth keeping that in mind.
Now, go have fun. In peace and quiet.