Warrior Priests:

Forced: The first point of damage assigned to this unit each turn is redirected to one target unit in any battlefield. (If there is no valid target, the damage is assigned to Warrior Priests.)

Blood for the Blood God

Action: Choose a target unit in any battlefield. Deal damage to that unit equal to its power.

My opponent played BftBG on my WP, outside of battle. Can that damage be redirected per the latter's action? I highlighted "assigned" because that seems to imply it is only a combat action. So we played that my WP died.

The relevant section is from page 17 of the rulebook, quoted verbatim:

Non Combat Damage

Outside of combat, some card effects also deal
damage to units or to a player’s capital. When these
effects resolve, this damage is first assigned and then
applied to the target in a manner similar to the way
damage is handled in combat. The one exception to
this rule is the Counterstrike keyword (see Counterstrike,
page 16). Counterstrike damage is always
applied as soon as it is assigned.

So no...your Warrior Priest would have survived to fight another day, provided that your opponent had units fielded in Battlefield zone.

Dang, I lost that battle.

Was losing your warrior priest pivotal in you losing that battle vs your opponent?

Yes

Post too short...

It's exciting to see that a game of Invasion can be that tight. Right down to the wire, or a cheap Warrior Priest, when deciding the victor. I can't wait to get my grubby hands on my copies.