Is the classification of sins into polytheism (shirk), innovation (bid‘ah), and major sins (kaba'ir)—such that polytheism is more dangerous than innovation, and innovation is more dangerous than major sins—correct? And does falling into innovation result in the non-acceptance of deeds?

The order mentioned is correct, as polytheism (shirk) is the most heinous sin, followed by innovation (bid'ah), then major sins (kaba'ir), and then minor sins (sagha'ir).

Ibn al-Qayyim mentioned in "Bada'i' al-Fawa'id" that Satan targets the son of Adam with six categories of evil, starting with disbelief (kufr) and polytheism (shirk). If he fails to achieve that, he moves on to innovation (bid'ah), which he prefers over immorality and disobedience due to its harm to religion, because it is a sin from which one does not repent, and it is considered a gateway to disbelief and polytheism. If he fails to achieve innovation, he moves on to major sins, then to minor sins, which may destroy their perpetrator if they accumulate.

This order confirms that innovations are more dangerous than acts of disobedience, but not every innovation is greater than every major sin.