Is a person held accountable for curses uttered in a moment of anger or suddenly without intent, or are the intrusive thoughts that pursue him in this regard an indication that he will not be held accountable?

Insulting Allah, the Messenger, or the religion is an act of disbelief (kufr) and apostasy from Islam, by consensus. The one who commits this act must offer sincere repentance, characterized by remorse and a firm resolve not to repeat it. If he repents, Allah will accept his repentance and forgive him, for Allah the Almighty says: (Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.") [Quran 39:53]. Thinking about whether the insult was intentional or not is a satanic whisper aimed at diverting you from repentance or weakening your fear of Allah. The anger that excuses a person is that which deprives him of the ability to distinguish right from wrong. Many who insult religion do not insult their own fathers, no matter how intense their anger, which indicates an emptiness of heart and a lack of veneration for Allah and His religion. Abandon these whispers; you have committed a grave evil, but you have before you a Merciful Lord who accepts the repentance of the penitent and transforms evil deeds into good ones. So strive in repentance and righteous deeds.