Usually you can press the Share button on the PS4 controller in order to share pictures and videos. Sadly, you will have to find other ways to do it in Persona 5 as it has been blocked.
Polygon reached out to Atlus USA to find out an explanation why the Share feature is blocked on Persona 5. You can read what the representative had to say about the situation below.
“This being a Japanese title with solely a single-playthrough story means Japan is very wary about it. Sharing is currently blocked through the native PS4 UI.”
The share feature will continue to be blocked even after the game is on sale. It feels as if they are doing this to avoid spoilers leaking out for Western gamers. People may have to use capture cards to record footage instead.