You check which creatures share a color with the target when the spell resolves.

Only one creature is targeted. If that creature leaves the battlefield or otherwise becomes an illegal target, the entire spell doesn’t resolve. No other creatures are affected.

A creature “shares a color” with any creature that is at least one of its colors. For example, a green-white creature shares a color with creatures that are green, white, green-white, red-white, black-green, and so on.

All creatures that share a color are affected, even your own.

If it targets a colorless creature, it doesn’t affect any other creatures. A colorless creature shares a color with nothing, not even other colorless creatures.

The targeted creature and the creatures that share a color with it at the time Incite Hysteria resolves gain an ability that says they can’t block this turn. It doesn’t matter if those creatures change colors before blockers are declared.