The Conciliar decree Lumen gentium does not say that Moslems have the faith of Abraham; it calls them fidem Abrahae se tenere profitentes ['they claim to ...']. Which is certainly true; Ibrahim is a very common Islamic name. The Conciliar text (signed, incidentally, by Archbishop Lefebvre) then does indeed go on to say that nobiscum Deum adorant unicum, misericordem, homines die novissimo iudicaturum. I take this to be an indication of an overlap between the attributes of the Gods of Islam and Christianity. Nostra aetate (3) I take to be engaging in this same process of analysis. If the Council had wished to make and impose a formal doctrinal statement of the identity of the God whom Christians worship, and the object of the Islamic cult, I presume that it would have needed to so clearly, unequivocally, and unambiguously. The Ecclesia docens has never left her dogmata definitive tenenda lurking in a clause within a statement uttered obiter. Deum cui Musulmani* cultum exhibent haec Sacrosancta Oecumenica Synodus sollemniter profitetur eundem esse quem Ecclesia Catholica adorat. Something similar to this would have needed to be said. The Conciliar Fathers could not, of course, say anything remotely like that, because we worship One God in Trinity and Trinity in Unity, which Moslems fiercely deny as blasphemous. By identifying common features of predication the Council implicitly assumes recognition of features of non-identity.
The Council, addressing the circumstances of its time, looked optimistically at what Islam and the true Faith could be said to hold in common. A different context could be said to require a different emphasis: of what radically divides two such different religions. This does not imply that the Council was wrong to say what it said, when it said it.
*Musulmani in Lumen gentium; they have metamorphosed into Muslimi in Nostra aetate.
I am reprinting a relevant earlier piece of mine.