Apparently gulping the faded Polaroid makes it unable to open the door in depths which I guess makes sense since you can't put it in the door if you swallowed it :
The Binding of Isaac: Rebirth - How To Unlock The Planetarium [Repentance DLC] - Steam Lists
How to Unlock Tainted Characters in Binding of Isaac
Everything To Guppy: Episode 669: Faded Polaroid on Apple Podcasts
Most Dmg Possible Binding Of Isaac | Peatix
The Best Binding of Isaac Seeds (Repentance and Afterbirth+) | Blog of Games
Faded Polaroid Stats : r/bindingofisaac
The Binding of Isaac: Repentance - The Easiest Way to Unlock The Planetarium