How do Catholics answer the question of idol worship within the faith?

From the good 'ol Catechim of Trent (or Catechism for Parish Priests; issued 1566) (under the First Commandment):

The Above Words Do Not Forbid All Images

Let no one think that this Commandment entirely forbids the arts of painting, engraving or sculpture. The Scriptures inform us that God Himself commanded to be made images of Cherubim, and also the brazen serpent. The interpretation, therefore, at which we must arrive, is that images are prohibited only inasmuch as they are used as deities to receive adoration, and so to injure the true worship of God.

They Forbid Idols And Representations Of The Deity

As far as this Commandment is concerned, it is clear that there are two chief ways in which God's majesty can be seriously outraged. The first way is by worshipping idols and images as God, or believing that they possessany divinity or virtue entitling them to our worship, by praying to, or reposing confidence in them, as the Gentiles did, who placed their hopes in idols, and whose idolatry the Scriptures frequently condemn. The other way is by attempting to form a representation of the Deity, as if He were visible to mortal eyes, or could be reproduced by colours or figures. Who, says Damascene, can represent God, invisible, as He is, incorporeal, uncircumscribed by limits, and incapable of being reproduced under any shape. This subject is treated more at large in the second Council of Nicaea. Rightly, then, did the Apostles say (of the Gentiles): They changed the glory of the incorruptible God into a likeness of birds, and of four-footed beasts, and of creeping things; for they worshipped all these things as God, seeing that they made the images of these things to represent Him. Hence the Israelites, when they exclaimed before the image of the calf: These are thy gods, Israel, that have brought thee out of the land of Egypt, are denounced as idolaters, because they changed their glory into the likeness of a calf that eateth grass.

When, therefore, the Lord had forbidden the worship of strange gods, He also forbade the making of an image of the Deity from brass or other materials, in order thus utterly to do away with idolatry. It is this that Isaias declares when he asks: To whom then have you likened God, or what image will you make for hill? That this is the meaning of the prohibition contained in the Commandment is proved, not only from the writings of the holy Fathers, who, as may be seen in the seventh General Council, give to it this interpretation: but is also clearly declared in these words of Deuteronomy, by which Moses sought to withdraw the people from the worship of idols: You saw not, he says, any similitude in the day that the Lord spoke to you in Horeb, from the midst of the fire. These words this wisest of legislators spoke, lest through error of any sort, they should make an image of the Deity, and transfer to any thing created, the honour due to God.

They Do Not Forbid Representations Of The Divine Persons And Angels

To represent the Persons of the Holy Trinity by certain forms under which they appeared in the Old and New Testaments no one should deem contrary to religion or the law of God. For who can be so ignorant as to believe that such forms are representations of the Deity? -- forms, as the pastor should teach, which only express some attribute or action ascribed to God. Thus when from the description of Daniel God is painted as the Ancient of days, seated on a throne, with the books opened before him, the eternity of God is represented and also the infinite wisdom, by which He sees and judges all the thoughts and actions of men. 'Angels, also, are represented under human form and with wings to give us to understand that they are actuated by benevolent feelings towards mankind, and are always prepared to execute the Lord's commands; for they are all ministering spirits, sent to minister for them who shall receive the inheritance of salvation. What attributes of the Holy Ghost are represented under the forms of a dove, and of tongues of fire, in the Gospel and in the Acts of the Apostles, is a matter too well known to require lengthy explanation.

They Do Not Forbid Images Of Christ And The Saints

But to make and honour the images of Christ our Lord, of His holy and virginal Mother, and of the Saints, all of whom were clothed with human nature and appeared in human form, is not only not forbidden by this Commandment, but has always been deemed a holy practice and a most sure indication of gratitude. This position is confirmed by the monuments of the Apostolicage, the General Councils of the Church, and the writings of so many among the Fathers, eminent alike for sanctity and learning, all of whom are of one accord upon the subject.

Usefulness Of Sacred Images

But the pastor should not content himself with showing that it is lawful to have images in churches, and to pay them honour and respect, since this respect is referred to their prototypes. He should also show that the uninterrupted observance of this practice down to the present day has been attended with great advantage to the faithful, as may be seen in the work of Damascene on images, and in the seventh General Council, the second of Nicaea.

But as the enemy of mankind, by his wiles and deceits, seeks to pervert even the most holy institutions, should the faithful happen at all to offend in this particular, the pastor, in accordance with the decree of the Council of Trent's should use every exertion in his power to correct such an abuse, and, if necessary, explain the decree itself to the people.

He will also inform the unlettered and those who may be ignorant of the use of images, that they are intended to instruct in the history of the Old and New Testaments, and to revive from time to time their memory; that thus, moved by the contemplation of heavenly things, we may be the more ardently inflamed to adore and love God Himself. He should, also, point out that the images of the Saints are placed in churches, not only to behonoured, but also that they may admonish us by their examples to imitate their lives and virtues.

Whenever I defend the Catholic faith I use the specific teachings and decrees from Church councils (especially the first 8 as they came before the Orthodox split) as much as possible as they form the basis for what is in the Catholic Catechism.

In the 8th ecumenical council (Constantinople 869-70) the decrees regarding images, statues, etc. were proclaimed. Taken from that council you will find the following decree (Canon 3):

"We decree that the sacred image of our lord Jesus Christ, the redeemer and saviour of all people, should be venerated with honour equal to that given to the book of the holy gospels. For, just as through the written words which are contained in the book, we all shall obtain salvation, so through the influence that colours in painting exercise on the imagination, all, both wise and simple, obtain benefit from what is before them; for as speech teaches and portrays through syllables, so too does painting by means of colours. It is only right then, in accordance with true reason and very ancient tradition, that icons should be honoured and venerated in a derivative way because of the honour which is given to their archetypes, and it should be equal to that given to the sacred book of the holy gospels and the representation of the precious cross.

And the consequence of not accepting this belief ...

If anyone then does not venerate the icon of Christ, the saviour, let him not see his face when he comes in his father’s glory to be glorified and to glorify his saints’, but let him be cut off from his communion and splendour; similarly the image of Mary, his immaculate mother and mother of God, we also paint the icons of the holy angels just as divine scripture depicts them in words; we also honour and venerate those of the highly renowned apostles, prophets, martyrs and holy men as well as those of all the saints. Let those who are not so disposed be anathema from the Father, the Son and the holy Spirit."

So by reading the above if a Catholic doesn't honor and venerate images, paintings, icons, etc. of Jesus, Mary, and the saints then you actually are not aligned with Church teaching. Now whether you agree with that is a different question, but 100% of what I believe as a Catholic is because the Church says so. Jesus built, protected, and gave authority to His Church, the Catholic Church, and to disbelieve the Church is to disbelieve Jesus.

Hope this helps.