Is there a way to force the player into an animation state using BP?

Sure. Using Animation Blueprints you can just set some variable on your player that gets checked each frame, and if true - pushes them to that animation state. Your level blueprint would then just turn that variable on/off, or whatever you wish. It all comes down to how you structure your animation state machine within the Animation Blueprint, but having game logic drive an animation state is a very easy and common thing to do.

Can I use level blueprints to force the player into a particular animation state? Like say I have a level trigger, and when the player touches it he is forced to enter a particular locomotion state.