"After you take an action, you may exhaust this support to choose an opponent. That opponent cannot take the same action that you just took on their next turn."

Scenario: I activate a character and exhaust running interference. Under no circumstance can my opponent activate a character, even if a they play a card that states activating a character or if they resolve a force speed/tactical mastery and use one of those actions to activate correct?

No. If they play a card which allows them to activate a character (e.g. Squad Tactics) then the action they took is Play a Card From Hand, not Activate a Character/Support. The card effect resulting in activation is not the same as taking that action.

The Tactical Mastery/Force Speed question is different. Running Interference prohibits that action for the entire turn, so if your opponent gets multiple actions they can't use any of those actions to take the prohibited action.