Whoever does not believe that the kaafirs are kaafirs is himself a kaafir

Yes, this is correct. Whoever is not convinced that the person who disbelieves in the religion of Allaah is a kaafir, does not believe what Allaah has told us about their being kaafirs, and he does not believe that the religion of Islam abrogates all previous religions and that all people must follow this religion no matter what their religion was before.

Allaah says (interpretation of the meaning):

And whoever seeks a religion other than Islam, it will never be accepted of him, and in the Hereafter he will be one of the losers [Aal Imraan 3:85]

Say (O Muhammad): O mankind! Verily, I am sent to you all as the Messenger of Allaah [al-Araaf 7:158]

Al-Qaadi Ayyaad said: hence we regard as a kaafir everyone who follows a religion other than the religion of the Muslims, or who agrees with them, or who has doubts, or who says that their way is correct, even if he appears to be a Muslim and believes in Islam and that every other way is false, he is a kaafir

(Al-Shifaa bi Tareef Huqooq al-Mustafaa, 2/1071)

Shaykh Muhammad ibn Abd al-Wahhaab (may Allaah have mercy on him) said:

Know that among the greatest things that can nullify Islam are ten things:

1. Associating othes in worship of Allaah alone, Who has no partner or associate. The evidence ofr that is the aayah (interpretation of the meaning):

Verily, Allaah forgives not (the sin of) setting up partners (in worship) with Him, but He forgives whom He wills, sins other than that [al-Nisaa 4:116].

This also includes offering scarifices to other than Allaah, such as to the jinn or at graves.

Whoever regards others as intermediaries between him and Allaah and calls upon them to ask them to intercede for him, is a kaafir according to scholarly consensus.

Whoever does not regard the Mushrikeen as kaafirs or doubts that they are kaafirs or regard their way as correct, is a kaafir according to scholarly consensus.

After enumerating them, he said (may Allaah have mercy on him):

In the case of all these things that nullify Islam, there is no difference whether a person is joking or is serious or is afraid except in cases where he is forced to do something. All of them are among the things that are very dangerous and which happen very often. The Muslim has to beware of them and fear them happening to him. We seek refuge with Allaah from the things that earn His wrath and His painful prunishment, May Allaah bless Muhammad.

(Muallafaat al-Shaykh Muhammad ibn Abd al-Wahhaab, 212, 213).

1. Shirk and kufr are the same when it comes to the ruling (hukm)

Ibn Hazm said:

Kufra and shirk are the same; every kaafir is a mushrik and every mushrik is a kaafir. This is the view of al-Shaafa and others.

(al-Fisl, 3/124).

The Jews and Christians are kuffaar and mushrikeen. Allaah says (interpretation of the meaning):

And the Jews say: Uzair (Ezra) is the son of Allaah, and the Christians say: Messiah is the son of Allaah. That is their saying with their mouths, resembling the saying of those who disbelieved aforetime. Allaahs Curse be on them, how they are deluded away from the truth! They (Jews and Christians) took their rabbis and their monks to be their lords besides Allaah (by obeying them in things which they made lawful or unlawful according to their own desires without being ordered by Allaah), and (they also took as their Lord) Messiah, son of Maryam (Mary), while they (Jews and Christians) were commanded [in the Tauraat (Torah) and the Injeel (Gospel)] to worship none but One Ilaah (God Allaah) Laa ilaaha illa Huwa (none has the right to be worshipped but He). Praise and glory be to Him (far above is He) from having the partners they associate (with Him). [al-Tawbah 9:30-31].

It was reported from Abu Hurayrag that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: By the One is Whose hand is the soul of Muhammad, not one of this nation, Jew or Christian, will hear of me and will die without having believed in that with which I have been sent, but he will be one of the dwellers of Hell fire.

(Narrated by Muslim, 153)

Whoever says that the Jews are not kaafirs is disbelieving in the words of Allaah (interpretation of the meanings):

And their hearts absorbed (the worship of) the calf because of their disbelief [al-Baqarah 2:93]

Among those who are Jews, there are some who displace words from (their) right places and say: We hear your word (O Muhammad) and disobey, and Hear and let you (O Muhammad) hear nothing. And Raaina [in Arabic it means Be careful, listen to us, and we listen to you, whereas in Hebrew, it means an insult] with a twist of their tongues and as a mockery of the religion (Islâm). And if only they had said: We hear and obey, and Do make us understand, it would have been better for them, and more proper; but Allaah has cursed them for their disbelief [al-Nisa 4:46]

Because of their breaking the covenant, and of their rejecting the Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) of Allaah, and of their killing the Prophets unjustly, and of their saying: Our hearts are wrapped (with coverings, i.e. we do not understand what the Messengers say) nay, Allaah has set a seal upon their hearts because of their disbelief, so they believe not but a little. And because of their (Jews) disbelief and uttering against Maryam (Mary) a grave false charge (that she has committed illegal sexual intercourse);  And because of their saying (in boast), We killed Messiah Eesaa (Jesus), son of Maryam (Mary), the Messenger of Allaah, but they killed him not, nor crucified him, but it appeared so to them the resemblance of Eesaa (Jesus) was put over another man (and they killed that man)] [al-Nisa 4:155-157]

Verily, those who disbelieve in Allaah and His Messengers and wish to make distinction between Allaah and His Messengers (by believing in Allaah and disbelieving in His Messengers) saying, We believe in some but reject others, and wish to adopt a way in between.  They are in truth disbelievers. And We have prepared for the disbelievers a humiliating torment [al-Nisa 4:150-151]

Whoever says that the Christians are not kuffaar is disbelieving in the words of Allaah (interpretation of the meanings):

Surely, in disbelief are they who say that Allaah is the Messiah, son of Maryam (Mary) [al-Maaidah 5:17]

Surely, disbelievers are those who said: Allaah is the third of the three (in a Trinity). But there is no Ilaah (god) (none who has the right to be worshipped) but One Ilaah (God Allâh). And if they cease not from what they say, verily, a painful torment will befall on the disbelievers among them [al-Maaidah 5:73]

And he is disbelieving in the words of Allaah concerning the Jews and Christians who do not believe in our Prophet or follow him:

Verily, those who disbelieve in Allaah and His Messengers and wish to make distinction between Allaah and His Messengers (by believing in Allaah and disbelieving in His Messengers) saying, We believe in some but reject others, and wish to adopt a way in between.  They are in truth disbelievers. And We have prepared for the disbelievers a humiliating torment [al-Nisa 4:150-151]

What is there left to say after these clear statements from Allaah, may He be exalted? We ask Allaah to guide us. May Allaah bless our Prophet Muhammad.