Is a person held accountable for bad thoughts and intrusive whispers that come to them involuntarily during worship concerning the soundness of religion, and do these thoughts affect the acceptance of their worship?

These thoughts do not exceed the level of waswasah (whispers of Satan/obsessive thoughts) and self-talk. Allah has overlooked them as long as they are not acted upon or spoken. The servant's dislike of these thoughts and waswasah is a sign of sound belief and strong faith. This is what the Prophet, peace and blessings be upon him, expressed as "pure faith." A person is not held accountable for waswasah if they repel it, do not believe in it, and do not act upon it. Striving against waswasah is a type of worship for which one is rewarded.