And Allah, Glorified is He, says:

“Invite to the way of your Lord with wisdom.” [Al-Nahl: 125]

It is not wisdom to call the polytheists to Allah by outwardly agreeing with them in matters belonging to their religion. Such conduct pleases them, and they use it as an argument against those who condemn their polytheism. This approach to calling people to Allah has no basis in the Quran or the Sunnah. Rather, the Quran indicates that one of the foundations of this call is to proclaim the truth openly whenever one is able. Allah Most High says:

“Then proclaim what you are commanded, and turn away from the polytheists. Indeed, We are sufficient for you against the mockers, who set up another god alongside Allah. They will soon know.” [Al-Hijr: 94–96]

And Allah knows best.

The foregoing makes clear the error of the proponent of this view: that prostrating before an idol does not constitute disbelief or polytheism—even if the person verbally acknowledges that he is prostrating to the idol, or outwardly demonstrates through this prostration his agreement with the polytheists in their religion—as long as he does not inwardly intend to prostrate to the idol.

Even more reprehensible is this proponent’s claim—as stated in the question—that “if an idolatrous polytheist recognizes the truth of Islam and acknowledges it, but, to appease his people and out of fear of blame and reproach, voluntarily prostrates with them to their idols, offers sacrifices to them, circumambulates them, outwardly venerates them, and does not openly disavow them, such a person is not to be judged a disbeliever, although he is sinful.”