Will one who rejected Islam due to a lack of inner conviction, and not out of obstinacy, enter the Fire? Is there a difference between someone who rejected Islam out of obstinacy and someone who rejected it due to a lack of conviction?

The disbelief of Jews and Christians is not necessarily due to obstinacy and arrogance. Their disbelief could be a disbelief of denial, or turning away, or doubt, or arrogance, or hypocrisy. The disbelief of denial is rare. As for the disbelief of arrogance and refusal, it is predominant among the enemies of the messengers, such as the Jews and Pharaoh, and Abu Talib's disbelief falls under this category. As for the disbelief of turning away (i'rad), it is neither affirming nor denying, but rather turning away from the Messenger. The disbelief of doubt is the lack of certainty in his truthfulness. As for the disbelief of hypocrisy, it is outwardly showing faith while inwardly concealing denial.