Free discussion and deception are fundamental parts of the game.
You may say anything you want at any point during the game, including giving away information, lying, misrepresenting, or challenging other players. When you hold secret information, such as information about your affiliation, you may tell the truth about that information, mislead or lie, or refuse to discuss it.
However, you may not actually reveal your character card at any point (since that would remove the possibility of tricking other players, which is fundamental to the game). In the same way, you may not try to "prove" you have a particular affiliation by describing the art on the card or other physical features. (Exception: If you use the inquisitor variant, the inquisitor player is sometimes allowed to look at another player's card.)