Should a Catholic visit the Abrahamic Family House in Abu Dhabi, where a church, a mosque, and a synagogue stand together?

No. Do not touch it with a ten foot pole. Your conscience is telling you the truth, because the two religions housed alongside the church disown Jesus Christ. You already have the right answer, brother. Do not touch it with a ten foot pole. Your conscience is telling you correctly. Trust it. Here is why it is telling you that. The whole premise of the place is that three faiths worship the same God under one roof, as equals, as three branches of one Abrahamic family. But two of those three deny that Jesus Christ is the Son of God. That is not a detail. St. John writes, "Who is a liar, but he who denies that Jesus is the Christ? This is Antichrist, who denies the Father and the Son. Whosoever denies the Son, the same has not the Father" (1 John 2:22 to 23). John is not using the word antichrist loosely. It applies to anyone who denies the Father or the Son, and in his own day he had the Jews and the heretic Cerinthus in view, who taught that Jesus was like God but not God. You cannot have the Father without the Son. There is no arrangement of architecture that makes that not true. John is also the one who gives the practical rule. "If any man come to you and bring not this doctrine, receive him not into the house, nor say to him, God speed you. For he that says to him, God speed you, communicates with his wicked works" (2 John 10 to 11). That is not about being rude to strangers. It is about not lending your presence to a false teaching, because your presence says something whether you intend it to or not. Now, somebody will tell you that this is just what the Church now does, and point to Nostra Aetate. Be careful there. Those Vatican II documents were written with a great deal of deliberate ambiguity, and I have said many times that God allowed that ambiguity to trap the men who wanted it. Nostra Aetate says the Buddhist searches for the divine in his religion. That is a statement of fact about what the man is doing. It does not say he finds Him, and it does not say he does not need the Catholic Church. The liberals read it the other way, and out of that reading came the interreligious prayer meetings at Assisi in 1986 and again in 2002, where the pope invited the Buddhists, the Zoroastrians, the Shintoists and the rest to pray to their gods for world peace. I have compared that to Solomon's apostasy, and I do not withdraw the comparison. Assisi is the direct ancestor of the Abu Dhabi house. On the Muslims specifically: if you are asking about monotheism, yes, they hold that God is one. If you are asking about the Trinity, the answer is no, and the Trinity is not an optional add-on to the God Christians worship. It is who He is. The Catechism could have been much more forthright about this instead of leaving the impression that a Muslim may hold his own concept of God with no obligation to consider the Christian God. And do not think ignorance covers an educated man. St. Paul says in Romans 1 that God's power and divine nature are plain from what has been made, and in Romans 2 that God wrote His law on their hearts, so they are without excuse. That is the honest Catholic position, and it is not cruelty; it is the reason we evangelize instead of building shared campuses. So, no, do not go. You are not being narrow. You are refusing to lend your body and your presence to a monument built on the proposition that it makes no great difference whether Jesus Christ is God. If you want to be near Muslims and Jews, be near them the way the Apostles were: as a Catholic who loves them enough to tell them the truth. That is a different thing entirely, and it is what our Lord asked of you. One more word, since you live nearby and this will come up again. No scenes, no letters, no arguing with the neighbors. Just decline. Keep your own house in order, go to Mass, and if anyone asks why you did not go, tell them plainly. That is usually more effective than an argument anyway.