Can a Catholic eat the food prepared for the Muslim Eid al-Adha?

Muslims do not worship the Holy Trinity. Their false god is an idol/demon (Ps. 95:5: "all the gods of the Gentiles are devils"). Thus, when they prepare food invoking this false god, it is indeed "a sacrifice to idols", even if it is done "in remembrance of Abraham."

As DJClayworth mentioned in his comment, 1 Corinthians 8:1-8 is the relevant scriptural reference. It is on how "things offered up to idols are not to be eaten, for fear of scandal." As St. Thomas Aquinas's commentary on these verses mentions, the meat itself is not bad (Titus 1:15: "all things are clean to the clean"), but the scandal that it may give to others for a Catholic to appear to be religiously adhering to a non-Catholic practice.

The May Catholics eat Muslim foods prepared for the Eid al-Adha?

Eid al-Adha is also called the “Sacrifice Feast” and it honors the willingness of Abraham to sacrifice his son, as an act of submission to God’s command. It marks the end of the Hajj pilgrimage to Mecca, the fifth Pillar of Islam. - What is Eid al-Adha?

The short answer is yes.

But that said one might avoid scandal, if in fact that possibility actually were to exist somewhere.

The Eid al-Adha is a dietary slaughter of certain animals and is not meat offered to idols, but is done in remembrance of Abraham’s willingness to sac rice his only son, Isaac.

Let us now look into the matter more deeply.

Eid al-Adha food is not offered to idols at all as the above quote demonstrates. The word sacrifice should really be slaughtered. On Eid al-Adha, which comes at the end of the hajj, or monthlong pilgrimage to Mecca, Muslims ritually slaughter a goat or other halal animal in memory of the ram Ibrahim sacrificed in place of his son. Part of the meat is eaten at the feast that is a highlight of the holy day. See here: A good weekend to be a Catholic goat

In fact, the world’s Catholic bishops at the Second Vatican Council approved Nostra Aetate declares that Catholics and Muslims have much in common.

In 1965, Pope Paul VI and the world’s Catholic bishops at the Second Vatican Council approved Nostra Aetate, the declaration on relations with non-Christian religions. The decree’s denunciation of calumny against Jews gets most of the attention, but it also proclaimed this:

“The church also regards with esteem the Muslims. They adore the one God, living and subsisting in himself, merciful and all-powerful, the Creator of heaven and earth,” although “they do not acknowledge Jesus as God” and regard him as only a prophet. The subsequent Catechism of the Catholic Church likewise defines the belief that “together with us [Muslims] adore the one, merciful God, mankind’s judge on the last day.”

Such interfaith concord is disputed by some conservative Protestants in the U.S. For example, the Christian Apologetics and Research Ministry believes the Catholic Church has “a faulty understanding of the God of Islam,” and Muslims “are not capable of adoring the true God.” Hank Hanegraaff of the “Bible Answer Man” broadcast — now a convert to Eastern Orthodoxy — has asserted that “the Allah of Islam” is “definitely not the God of the Bible.” [Note that “Allah” is simply the Arabic word meaning “God.”] - This is not a trick question: Do Christians and Muslims worship the same God?

How could it be not permitted when Catholics in Muslim countries deal with this subject in a different way:

The Indonesian government set June 25 for Eid al-Fitr this year. Indonesia traditionally celebrates Eid al-Fitr over two days.

Many churches located next to mosques — including Jakarta’s St. Mary of the Assumption Cathedral — postponed Mass June 25 so as not to interfere with Eid prayers. Catholics — including bishops, priests, nuns and laypeople — also visited and greeted Muslims at mosques and in their homes.

Archbishop Antonio Filipazzi, papal nuncio to Indonesia, paid a courtesy call on Indonesian President Joko Widodo after attending Eid prayers at Istiqlal Mosque in Jakarta.

Archbishop Robertus Rubiyatmoko of Semarang visited Muslims attending Eid prayers at Central Java Grand Mosque to foster “fraternity among the people of Indonesia.” Other bishops also visited local Muslims leaders.

“I hope that interfaith life in the archipelago, especially in Central Java, will be much better in future, so that peace and joy can be established,” Archbishop Rubiyatmoko said.

At churches across Indonesia, Christians offered lunch or gift parcels for poor Muslim families.

In Jakarta, the archdiocese and Community of Sant’Egidio organized an Eid al-Fitr lunch at the Friendship House in West Jakarta for 160 poor Muslim children and their families.

“The poor hardly ever have the chance to sit together for meals. So we invited them so they could sit and eat together,” said Piere Doe, coordinator of the event. - To ease tensions, Indonesian Catholics help Muslims celebrate Eid al-Fitr

According to the Church, Muslim halal meat is not sacrificed to idols at all.

The Roman Catholic Church does not teach that food certified by either the appropriate Jewish authorities as meeting requirements for Kosher certification, or by Islamic authorities as meeting requyirements for Halal certification are foods offered to idols. The Catholic position is that the God of the Jews and the God of Muslims is the same God as the Christian God,, and therefore not an idol.

In explaining different understandings between most Jews and most Muslims, from the understanding that most Christians have of God, Catholics teach that Jews and Muslims, and frankly many non-Catholic Christians, too, have (at best) an incomplete knowledge of the nature of God. - According to the Roman Catholic Church, is halal meat being offered up to idols?

AthanasiusOfAlex comment to this same answer follows as such:

Muslims do not assert that thereby they are offering a sacrifice to God. They are simply fulfilling their dietary requirements. That is very different from the situation described in Acts and 1 Corinthians.

Pakistan Church offers Eid guidelines on sacrificial meat:

Father Inayat Bernard, rector of Lahore's Sacred Heart Cathedral, condemned those who term the Muslim feast as "the devil's sacrifice." "Such misconceptions are spread by semi-literate church leaders during this time of the year. They use selected Biblical verses to prove that this feast honors the devil," he told his congregation on Aug. 19.

"This is Sunnat-e-Ibrahimi (Abrahamic tradition) and relates to a prophet who was revered by three major religions. It is a pure diet and there is no harm in eating it. But do not force others to do so.

"We should abide by cultural norms and share the happiness of our Muslim siblings. It is a part of living the interreligious dialogue as per Vatican Council II teachings. Nothing is haraam (prohibited and sinful) for us except those things that come out of the human body as stated in the Bible.”

His sermon was part of a church awareness drive as Muslims in Pakistan finalize preparations for the Islamic festival from Aug. 22-24. - Pakistan Church offers Eid guidelines on sacrificial meat

The Church presently lacks an absolute definitive answer on the subject: In unitas, in dubiis libertas, in omnibus caritas. End result would be that it is permitted to eat such foodstuffs, but at the same time scandals should also be avoided if occasioned in some particular circumstance.

Addendum*

What exactly do Muslims say when they slaughter halal animals?

It is more exactly the recitation of one of their verses: "In the name of God, the Most Gracious, the Most Merciful".

The Basmala (Arabic: بسملة‎ basmalah), also known by its incipit Bismillāh (Arabic: بِاسم الله‎, "In the name of God")[1], is the Islamic phrase bi-smi llāhi r-raḥmāni r-raḥīm بِسْمِ اللهِ الرَّحْمٰنِ الرَّحِيْمِ "In the name of God, the Most Gracious, the Most Merciful".

This is the phrase recited before each surah (chapter) of the Qur'an – except for the ninth. It is used by Muslims in various contexts (for instance, during daily prayer) and is used in over half of the constitutions of countries where Islam is the official religion or more than half of the population follows Islam, usually the first phrase in the preamble, including those of Afghanistan, Bahrain, Bangladesh, Brunei, Egypt, Iran, Iraq, Kuwait, Libya, Maldives, Pakistan, Tunisia, and the United Arab Emirates. - Basmala (Wikipedia)

The method of slaughter is as follows:

The food must come from a supplier that uses halal practices. Dhabīḥah (ذَبِيْحَة) is the prescribed method of slaughter for all meat sources, excluding fish and other sea-life, per Islamic law. This method of slaughtering animals consists of using a well-sharpened knife to make a swift, deep incision that cuts the front of the throat, the carotid artery, trachea, and jugular veins. The head of an animal that is slaughtered using halal methods is aligned with the qiblah. In addition to the direction, permitted animals should be slaughtered upon utterance of the Islamic prayer Bismillah "in the name of God". Halal (Wikipedia)

Arabic-speaking Christians sometimes use the name Basmala to refer to the Christian Trinitarian formula "In the name of the Father, the Son and the Holy Spirit", as in the tradition of the Ethiopian Orthodox Church.