Is respecting and/or worshiping the black stone of Kaaba an important part of Islam in order to please God to gain his favor?
Like when a scholar specifically goes to the black stone and kisses it.
Bukhari, Muslim and Abu Daw'ud reported that 'Umar approached the Black Stone and kissed it.
Then he said:
"I know that you are a mere stone that can neither harm nor do any good. If I had not seen the Prophet (peace be upon him) kissing you, I would have never kissed you."
So basically, it's ONLY done because the Prophet did it.
Worshipping anything but Allah is shirk, but kissing and touching and etc. aren't shirk, as kissing and touching are not among the worshipping behaviors.
Also the black-stone is not what is thought about, it is believed according to Shia Ahadith that the black stone was indeed a white stone from Heaven which turned into black due to wrongdoings of Adam's children, and the white stone is indeed an angel, one among the highest ranked angels, the first who accepted the covenant between Allah and His angels, so that Allah chose him as the most trustworthy one to preserve the covenant of His other creatures, so was sent out from the Heavens toward the Earth after the Covenant day before Adam's descension to the Earth. All the humans' covenant in there kept inside that stone and people are told to touch it every year (although it is not obligatory) during Hajj, like renewing the allegiance to Allah, so that the black-stone is like the God's hand on the Earth. [You can find one such Hadith in Kaafi, v.4, p.185, although I have seen other such Ahadith as well]
Note that according to the Quran consciousness is not limited to what we know as a live-species, even stones are alive but to being alive to an extent not understandable to our material senses. You can see it e.g. when Allah informs us like the followings:
Whatever is in the heavens and on earth, doth declare the Praises and Glory of Allah,- the Sovereign, the Holy One, the Exalted in Might, the Wise. [62:1]
And there are many other verses reporting the same news. Note the "whatever" instead of "whoever" in a verse like this:
Seest thou not that it is Allah Whose praises whoever in the heavens and on earth do celebrate, … . [24:41]
And Allah the Wise never use a word unless there is an intention before that. Also note the following verses:
That Day shall We set a seal on their mouths. But their hands will speak to us, and their feet bear witness, to all that they did. [36:65]
They will say to their skins: "Why bear ye witness against us?" They will say: "Allah hath given us speech,- (He) Who giveth speech to everything: He created you for the first time, and unto Him were ye to return. [41:21]
Then the word went forth: "O earth! swallow up thy water, and O sky! Withhold (thy rain)!" and the water abated, and the matter was ended. The Ark rested on Mount Judi, and the word went forth: "Away with those who do wrong!" [11:44]
And last but not least, note that all the fake gods (with the exception of a few, like Jesus, Uzeir, the Virgin Mary, PBUT) would be sent to the hell for being worshipped:
If these had been gods, they would not have got there! but each one will abide therein. [21:99]
And even there is a Hadith that an idol of Arabs in Mecca was appeared to Imam Ali --peace be upon him-- as a black ugly man and was killed by him according to an order from the holy prophet to Imam, then the idol was found as broken by people in the city.
Anyway, there are things that we know and there are things that we think we know and there are things that we don't know at all. If respecting a person or kissing a family member (kissing being a manner to show liking or respect) is considered as shirk then kissing and touching the black stone and many other things (seemingly non-alive species) may be shirk as well, otherwise if someone accuse a Muslim for shirk and cannot prove it he will be stopped to be questioned in the Judging day.
(Shia Islam view)
Shia believes the black stone is more than a stone and also believe grave of prophet and Imams are more than the black stone.
Also Quran says the shirt of prophet Yusuf (PBUH) did cure the blind eyes of his father. So there are more sacred things that are blessed and can be kissed.
Dawud ibn Salih says: "[The Caliph] Marwan [ibn al-Hakam] one day saw a man placing his face on top of the grave of the Prophet. He said: "Do you know what you are doing?" When he came near him, he realized it was Abu Ayyub al-Ansari. The latter said: "Yes; I came to the Prophet, not to a stone."
Ibn Hibban in his Sahih , Ahmad (5:422), Tabarani in his Mu`jam al-kabir (4:189) and his Awsat according to Haythami in al-Zawa'id (5:245), al-Hakim in his Mustadrak (4:515); both the latter and al-Dhahabi said it was sahih. It is also cited by al-Subki in Shifa' al-siqam (p. 126), Ibn Taymiyya in al-Muntaqa (2:261f.), and Haythami in al-Zawa'id (4:2).
Reference and more evidences:
It is part of mainstream Sunni and Shia versions of Islam, but it is not part of Islam as taught by the Quran. Never once has this stone been mentioned anywhere in the Quran.