When BLU captures a point, it calls the team_control_point's OnCapTeam2 output.
You can use this to call inputs on other entities, such as disabling old spawn points and enabling new ones.
For a shortcut door instead, you would make the func_door without any opening triggers. Instead, you would call its Open input from the point's OnCapTeam2 output.
Note: If you're doing a lot of actions, consider putting it in a logic_relay and Trigger that instead.