Plot hole: Thomas Riker is able to steal the Defiant partially because he's a genetic double for and not a clone of Will Riker. Thomas Riker's existence is not a secret. Star Fleet is aware that the first officer of their flagship has a genetic duplicate who resigned and is out there somewhere. There should be something in place to verify Will's location before giving Thomas access. But then, of course, we wouldn't have an episode.
Suggested correction: At this point Thomas Riker is still a Starfleet officer. There is no need to lock him out of accessing the Defiant's systems as he is considered just as trustworthy as Will.
It's said that he resigned over suspected Maquis sympathies. They were right.
They say that he had expressed political opinions that supported the Maquis, not that he had resigned from Starfleet. A large number of Starfleet officers supported the Maquis' intentions, but still stayed loyal to Starfleet.
No, Thomas Riker accessed the Defiant under the guise of being Will Riker, and Major Kira released the lockouts being under that impression.
Exactly. NOBODY in Star Fleet has thought "Well, what if one of them claims to be the other? How do we tell them apart?"