As for accepting the other, in order to merely know his opinions, without pronouncing judgments against him, and without refuting what he says, is not of the Islamic method whatsoever. Rather, what the Book indicates is completely contradictory to that. When the Noble Qur'an "They say: 'Ar-Rahmaan has begotten a child.' Indeed you have brought forth a terrible evil thing! Whereby the heavens are almost torn down, the earth split asunder and the mountains fall in ruin. That they ascribe a child to Ar-Rahmaan. And it is not suitable for Ar-Rahmaan to beget a child" [TMQ Maryam: 88-92].

"And they say: 'When will this promise (come to pass), if you are truthful?' If only those who disbelieved knew when they will not be able to ward off the Fire from their faces nor their backs. Nor will they be helped. Nay, it will come upon them suddenly and perplex them. And they will have no power to avert it nor will they get respite" [TMQ Al-Anbiya: 38-40].

And:

"And when you said: 'O Musa, we shall never believe in you until we see Allah plainly.' And you were seized with a thunder bolt while you were looking" [TMQ Al-Baqarah: 55].

And:

"And when it was said to them: 'Believe in what Allah revealed', they said: 'We believe in what was revealed to us' and they disbelieve in what is after it while it is the truth confirming that which is with them. Say: 'Why then did you kill the Prophets of Allah aforetime if you were (indeed) believers?'" [TMQ Al-Baqarah: 91].

"And they say: 'None shall enter Paradise except he be a Jew or Christian.' Those are their desires. Say: 'Produce your proof if you are truthful.' Rather whoever submits his face to Allah and is a doer of good, his reward is with Allah. Such will not fear nor will they grieve" [TMQ Al-Baqarah: 111-112].

"And they say: 'Allah has begotten a child.' Glory be to Him! Nay, to Him belongs all that is in the heavens and the earth. All surrender to Him with obedience" [TMQ Al-Baqarah: 116].

And:

And they say: 'Be Jews or Christians (then) you will be guided.' Say: 'Nay, the creed of Ibrahim, and he was not of the polytheists'" [TMQ Al-Baqarah: 135].

"Have you not considered about he who disputed with Ibrahim about his Lord because Allah had given him the kingdom? When Ibrahim said to him: 'My Lord is He who gives life and causes death.' He said: 'I give life and cause death.' Ibrahim said: 'Verily Allah causes the sun to rise in the east thus you cause it to rise in the west.' Thus the disbeliever was utterly defeated. And Allah guides not the unjust folk" [TMQ Al-Baqarah: 258]. Even though this ayah was of the Shar'a of those before us, however it commenced with His saying subhanahu:

And:

"Those who said about their brothers while they sat (at home): 'Had they obeyed us, they would not have been killed.' Say: 'Avert death from yourselves if you speak the truth!'" [TMQ Al-Imran: 168].

And:

"Those who said: 'Verily Allah has taken our promise not to believe in any Messenger unless he brings to us an offering which fire devours.' Say: 'There came to you Messengers before me with clear proofs and with what you speak of. Why then did you kill them if you are truthful?'" [TMQ Al-Imran: 183].

And:

"And the Jews say: 'Allah's hand is tied up!' Be their hands tied up and be they accursed for what they say! Nay, both His hands are widely outstretched. He spends as He wishes" [TMQ Al-Mai’dah: 64].

And:

"Those who associate (with Allah) will say: 'If Allah had willed, we would not have associated nor would we have forbidden anything.' Likewise belied those before them until they tasted Our wrath. Say: 'Have you any knowledge so that you produce it for us? Verily you follow nothing but conjecture (dhann) and you do nothing but lie" [TMQ Al-An’am: 148].

And:

"And the Jews say: 'Uzayr is the son of Allah' and the Christians say: 'The Messiah is the son of Allah.' That is their saying from their mouths. They imitate the saying of those who disbelieved of old. Allah's curse is upon them, how they lie! They took their rabbis and monks as lords besides Allah and the Messiah son of Mary while they were not commanded save to worship one Lord. There is no god but He. Glorified is He beyond what they associate!" [TMQ At-Taubah: 30-1].

And:

"And when Our clear aayaat are recited to them, those who expect not meeting Us say: 'Bring us a Qur'an other than this or change it.' Say: 'It is not for me to change it of my own accord. I only follow that which was revealed unto Me. Verily I fear, if I disobey my Lord, the punishment of a Great Day.' Say: 'If Allah had so willed, I should not have recited it to you nor would He have made it known to you, I had stayed among you a lifetime before this. Have you then no sense?'" [TMQ Yunus: 15-6].

And:

"And they say: 'There is nothing but our life of this world, we die and we live and nothing destroys us except time. They have no knowledge of it, they only conjecture. And when Our clear aayaat are recited to them, their argument is not other than that they say: 'Bring back our fathers if you are truthful.' Say: 'Allah gives you life then causes you to dies, then He will assemble you on the Day of Resurrection about which there is no doubt but most of mankind know not'" [TMQ Al-Jathiya: 24- 6]. Even the aayaat of Surah Al-Kahf, which one of them used as evidence, does not depart from this style of refuting the concept or concepts of kufr. Nor is the dialogue, as they say, a mere intellectual process only; rather it is understanding and refuting the concepts of kufr. This is clear in the rebuke of the companion, rejecting the kufr of one of the two, saying:

Do you disbelieve in He who created you dust then out of a (nutfah) then fashioned you a man? But as for me, He is Allah my Lord and none shall I associate with my Lord. Had you, when you entered your garden, only said: 'Whatever Allah wills (will occur), there is no power except with Allah.' If you see me less than you in property and children, perhaps my Lord will give me better than your garden and send upon it a (husband) from the sky, then it will be a slippery earth. Or its water

becomes deep sunken so that you will not be able to seek it" [TMQ Al-Kahf: 37-41]. So how can it be said that the companion did not pronounce judgment while he rebukes him saying: 'Do you disbelieve in your creator?' Then he directs him to what is obliged upon him to say namely: 'Whatever Allah wills, there is no power except with Allah.' Then he explained to him the power of the All-Capable (Al-Qadir) Creator to send the bolt (from heaven) and make the water disappear. So how can it be said that this is a model of religious dialogue without restriction or condition, without pronouncing judgments and accepting the other as he is?

As for the one using as evidence His (SWTH) saying:

Say: 'O you disbelievers! I do not worship that which you worship. And you do not worship what I worship'" [TMQ Al-Kafirun: 1-3] for dialogue with disbelievers (kuffar) and His ﷺ saying:

"If one of the polytheists seeks your protection, grant him protection until he hears the word of Allah; then escort him to a place of safety" [TMQ At-Tawbah: 6] for dialogue with polytheists; this is an incorrect deduction and outside its context. Surat Al-Kafirun has pronounced a judgment against them, which states that they are kuffar and will remain upon their kufr without ever believing. Allah subhanahu knew that they would never believe ever and He informed the Messenger of Allah ﷺ about that. He commanded him to convey it to them in order to offer their mutual exchange of duties. So there remains no place for dialogue whatsoever after Allah subhanahu informed that they would remain disbelievers until death. This Surah descended regarding specific people. Allah spoke the truth. Some of them disbelieved and some of them were killed; and none of them believed.

As for HIs (SWTH) saying:

"If one of the polytheists seeks your protection, grant him protection until he hears the word of Allah; then escort him to a place of safety" [TMQ At-Tawbah: 6]. There is no evidence in this ayah for what they claim about dialogue between equals. There is no indication therein for dialogue; rather, therein is a command to make the polytheist hear the word of Allah, and either he believes or he is escorted to his place of safety. So the ayah is about giving protection to the polytheist who wishes to ask about Islam, so Islam is explained to him in a way that is hoped he will embrace it. There is no evidence in the ayah for dialogue in order to know his opinions in the way of equality and equivalence without pronouncing judgment against him. The ayah determines that he is a polytheist, so it pronounced judgment of polytheism. It does not come to listen to his opinions; rather, it seeks making him listen to the Qur'an. So there is no sense in using it as evidence.