To what extent is it correct to assert the obligation of declaring an innovator (mubtadi') to be an innovator (tabdī'), and that whoever does not declare him an innovator is himself an innovator? And does this include the scholar, the common person, and the student of knowledge? And does it include the innovator whose declaration of innovation is disputed among the people of the Sunnah?

The rule mentioned in the question was not reported, nor was it used by the Salaf or the people of knowledge. Furthermore, the Salaf differed on many innovations (bid'ah) and did not declare each other innovators. It has not been narrated from any of the people of knowledge that they declared an innovator someone who did not declare the perpetrator of an innovation an innovator.

It appears that this rule was modeled after the principle, "Whoever does not declare a disbeliever a disbeliever is himself a disbeliever." However, the people of knowledge clarified that declaring someone who does not declare a disbeliever a disbeliever applies only to universally agreed-upon disbelief.

Nevertheless, it is imperative to denounce the evil (munkar) perpetrated by the innovator, strive for their guidance, and warn against innovations in general. The Prophet, peace and blessings be upon him, warned against them by saying: "Every newly invented matter is an innovation (bid'ah), and every innovation is misguidance, and every misguidance is in the Hellfire." He also said: "Indeed, Allah has withheld repentance from every innovator," meaning He has prevented them from repenting.