Pagan origin arguments usually divide into 2:
1) Those arguments like moon God, Hubal, Rahman, etc. These are more than sufficiently addresses in the Islamic awareness website:
2) Those arguments which show that the Quraysh did similar practices. For instance, the Quraysh used to do Hajj, but they did it naked. They also used to do the talbiyah differently. The Ka'bah was special to them, etc.
Here we respond by saying that these were originally instituted by Abraham, but the Quraysh came and introduced their kufr into it. Islam came and either 1) Eliminated it entirely or 2) Rectified the practice by boosting out the kufr elements from them.
What is the Black Stone? Black Stone (al-Hajr al-Aswad) is a Holy Stone placed in the Holy Ka'ba.
What is it for? When Muslims go for pilgrimage to Makkah this acts as starting point for circumambulating the Holy Ka'ba and has some symbolic significance.
As I mentioned it marks the start point of the circumambulation (tawaaf) of the Holy Ka'ba. Those who circumambulate in the immediate place around Ka'ba kiss it while those who cannot make up-to it just wave their hands towards it while there are people who circle the Ka'ba even from the first, second floors as well. They follow the mark parallel to the Black Stone as the start point of the tawaaf. Had there been something too special in this stone itself than it would have been mandatory for each and every pilgrim to physically touch and kiss which is not the case.
As its serves as a mark to something important so its just as if a soldier or some other person returns to his homeland after a long time so he kisses the soil of his land or shows admiration for some landmarks. Its his love, his affection for his homeland and nothing more. For itself soil is nothing, same way Black Stone for itself is nothing.
Do Muslims worship the Black Stone? No Muslims don't! The purpose of the Black Stone has been described above. Further there is more historic evidence that its not an object of Worship. In one of most sad events of Islamic history the city of Makkah was sacked by the Qaramatians in the year 930 C.E. They killed many pilgrims, desecrated the holy sites and took away the Black Stone to their seat of Power at Al-Hasa in Bahrayn. It was restored in the year 952 C.E. thus for about quarter of a century the stone was displaced from its location yet neither did Muslims turn to Al-Hasa for prayers during that period neither were the obligations of Salah (ritual prayers) and Hajj (obligatory pilgrimage) suspended. If it were an object of worship much consternation would have followed the unfortunate event.
Why kiss it? And we Muslims kiss it just because of Holy Prophet Muhammad (PBUH) did it.
Read the following Hadith, it makes the whole thing crystal clear.
عَنْ عَابِسِ بْنِ رَبِيعَةَ عَنْ عُمَرَ رَضِيَ اللَّهُ عَنْهُ
أَنَّهُ جَاءَ إِلَى الْحَجَرِ الْأَسْوَدِ فَقَبَّلَهُ فَقَالَ إِنِّي أَعْلَمُ أَنَّكَ حَجَرٌ لَا تَضُرُّ وَلَا تَنْفَعُ وَلَوْلَا أَنِّي رَأَيْتُ النَّبِيَّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يُقَبِّلُكَ مَا قَبَّلْتُكَ
Narrated 'Abis bin Rabia: 'Umar came near the Black Stone and kissed it and said "No doubt, I know that you are a stone and can neither benefit anyone nor harm anyone. Had I not seen Allah's Apostle kissing you I would not have kissed you."
(Bukhari Hadith 1494)
Similar has been narrated about the First Caliph, Abu Bakr (RA). See Suyuti's Tarikh Al-Khulafa 1/35 cf. Ilal al-Darqutni
Catholic concept of Mary:
Contrary to the Islamic concept of showing respect to this stone what the Christians do is much more than this.
Firstly, making the idols of any holy person and its revering is no way comparable to Muslim's kissing the shapeless stone which for itself signifies nothing.
Secondly, Catholics do pray 'To Jesus through Mary' thus believing in her as at least an intercessor. See THIS
I am saying 'at least' because this is something no catholic would ever deny. There were and still are people who openly called Mary, 'the Mother God', not merely 'Mother of God'. And even today there are people still who revere and venerate her as "GOD". And such people claim to be Catholics .
So showing veneration to the statue of Mary (May ALLAH bestow His blessings upon her) is nothing less than idol worship. No Muslims, even the most lunatic of them has any such belief about the Black Stone or the Holy Ka'ba. Thus such a concordance is nothing but mere absurdity.
Islam doesn't claim to bring everything new with it, so of course there is going to be these Pre Islamic practices from before. However Muslims do prayer differently, fast differently, etc.