Q: If I use Even Death May Die to take a Keeper out of the discard and play it, can that Keeper play be stopped by Twist Of Fate?

A: No. To refresh on what those cards do:

Even Death May Die (Action) says “Search through the discard pile. Take any Action or investigator Keeper you wish, and immediately play it. (Anyone may look through the discard pile at any time, but the order of what’s in the pile should not be changed)”

Twist of Fate (Surprise) says “Out of Turn: When another player plays a Keeper, it goes in front of you instead of them, possibly preventing their victory. During your turn: Steal another player’s Keeper and put it in front of you.”

Because it was an Action which precipitated this Keeper being put in front of you, and Twist of Fate does not stop Actions, your opponent would have to have used The Stars Are Wrong to counter Even Death May Die… and the result would be that the Keeper you tried to take out of the trash would simply remain in the trash.