With this trinket equipped, I was kicked out of the game through an error for the first time ever within my 80+ hours of game play. I have no idea if there is a correlation. But other than that I saw no discernible effects.
Upon opening Isaac again, and pressing continue, the level was reset. NO! was no longer in my inventory. I played through the level again and found that all item drops were exactly the same. I picked up NO! again and when I tried to go into a store, my game crashed just as before. I will now attempt to go into the store without the trinket and see if there is a different result.
Without the trinket, I was able to successfully enter the shop. NO! perhaps prohibits certain rooms from being entered? Unfortunately I died on Krampus while trying to see if devil rooms were prohibited. I am unsure as to what the full effects are of this trinket but from what I've seen, it isn't very helpful and I hope that I am wrong about its actual effects.