The Catholic Church as Mystery Babylon
Who is the harlot ?
Revelation 17:18 KJV  And the woman which thou sawest is that great city, which reigneth over the kings of the earth.
So the woman is a great city that reigns over kings.
Which city are the talking about ?
Revelation 17:9,15 KJV  And here is the mind which hath wisdom. The seven heads are seven mountains, on which the woman sitteth.
So the woman is a great city that sits on seven mountains.
Tradition holds that Romulus and Remus founded the original city on the Palatine Hill on April 21, 753 BC, and that the seven hills were first occupied by small settlements that were not grouped. The seven hills' denizens began to interact, which began to bond the groups. The city of Rome, thus, came into being as these separate settlements acted as a group, draining the marshy valleys between them and turning them into markets (fora in Latin). Later, in the early 4th century BC, the Servian Walls were constructed to protect the seven hills. 
- Seven hills of Rome, https://en.m.wikipedia.org/wiki/Seven_hills_of_Rome
So we can see that even in ancient times they were aware of that Rome sits on 7 hills.
What do they mean by many waters ?
Revelation 17:1 KJV  And there came one of the seven angels which had the seven vials, and talked with me, saying unto me, Come hither; I will shew unto thee the judgment of the great whore that sitteth upon many waters:
Some people would say that it cannot be Rome because Rome doesn’t sit on many waters.
Revelation 17:15 KJV  And he saith unto me, The waters which thou sawest, where the whore sitteth, are peoples, and multitudes, and nations, and tongues.
But the waters are explained to be peoples. And the Roman Catholic Church have members in many nations and these members speak different tongues.
the blood of the martyrs
Revelation 17:6 KJV  And I saw the woman drunken with the blood of the saints, and with the blood of the martyrs of Jesus: and when I saw her, I wondered with great admiration.
That it is the Roman Catholic Church that is talked about also fits with that she is drunken with the blood of the martyrs. Because of the Roman Catholic inquisition.
Scarlet and purple
Revelation 17:4 KJV  And the woman was arrayed in purple and scarlet colour, and decked with gold and precious stones and pearls, having a golden cup in her hand full of abominations and filthiness of her fornication:
Higher priests in the Roman Catholic Church wear purple and scarlet clothing.
Cardinals Walter Kasper (left) and Godfried Danneels (right) wearing their choir dress: scarlet (red) cassock, white rochet trimmed with lace, scarlet mozetta, scarlet biretta (over the usual scarlet zucchetto), and pectoral cross on cord. 
- Cardinal catholic church, https://en.m.wikipedia.org/wiki/Cardinal_(Catholic_Church)
Scarlet has been a color of power, wealth and luxury since ancient times. Scarlet dyes were first mentioned in 8th century BC, under the name Armenian Red, and they were described in Persian and Assyrian writings. The color was exported from Persia to Rome. During the Roman Empire, it was second in prestige only to the purple worn by the Emperors. Roman officers wore scarlet cloaks called paludamenta, and persons of high rank were referred to as the coccinati, the people of red. 
The ancient Roman calix was a drinking vessel consisting of a bowl fixed atop a stand, and was in common use at banquets. In Roman Catholicism, Eastern Orthodox Church, Oriental Orthodoxy, Anglicanism, Lutheranism and some other Christian denominations, a chalice is a standing cup used to hold sacramental wine during the Eucharist (also called the Lord's Supper or Holy Communion). Chalices are often made of precious metal, and they are sometimes richly enamelled and jewelled. The gold goblet was symbolic for family and tradition. 
Golden cup can be used in the Roman Catholic Eucharist.
Revelation 17:5 KJV  And upon her forehead was a name written, MYSTERY, BABYLON THE GREAT, THE MOTHER OF HARLOTS AND ABOMINATIONS OF THE EARTH.
This term is most often used among Catholics as Holy Mother Church. The Church is considered to be a mother to her members because she is the Bride of Christ, and all other churches have had their origin or derived from her. Another term used in the Catechism is the title "Mater et Magistra" (Mother and Teacher). Pope John XXIII made this the title of his encyclical celebrating the seventieth year after Leo XIII's groundbreaking social encyclical, explaining that in this Mother and Teacher all nations "should find ... their own completeness in a higher order of living." Pope Francis said:The Church is our mother. She is our "Holy Mother Church" that is generated through our baptism, makes us grow up in her community and has that motherly attitude, of meekness and goodness: Our Mother Mary and our Mother Church know how to caress their children and show tenderness. To think of the Church without that motherly feeling is to think of a rigid association, an association without human warmth, an orphan. 
- Mother church, https://en.m.wikipedia.org/wiki/Mother_church
The pope describes the Catholic Church as the mother of the members of the Catholic Church.
So what should we as christians do ?
Since the ecumenical movement is in full force today with the end goal to unify all christian denominations with the catholic church.
The right way as a christian fundamentalist is to separate from the churches.
(Revelation of John 18:4 [KJV]) And I heard another voice from heaven, saying, Come out of her, my people, that ye be not partakers of her sins, and that ye receive not of her plagues.