“Do you deny that the traditional Catholic doctrine is that your superiors should be obeyed to the best of your ability unless they command you to sin?”
I don’t deny it all. But, for any good Catholic to sign off on a magisterial document that states he worships the same god as the Muslims worship is a sin against the First Commandment. Muslims deny the Holy Trinity, the Divinity of Christ, etc.
Now as far as the pledge; unless you know what exactly that pledge is, you’re still talking nonsense. Why do you think the Vatican has insisted that both parties keep the preamble a secret until a deal is done, if ever?
I've posted extensively on this elsewhere. The passage you're referencing does not use the words "the same god". You can argue that that's what it means, but that's your opinion and nothing more.
The actual language says, "[Muslims] profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind's judge on the last day".
So, let's stipulate as to some facts:
Even if Nostra Aetate were infallible (and I don't think it is), the above is all that it could claim. Why? The Catholic magisterium's charism of infallibility extends to the teaching of Catholicism, not to the teaching of any other religion. Claiming anything like "Muslims and Catholics worship the same god" is making claims about Muslim teaching which are far beyond merely stipulating commonly known facts, and which are far beyond the magisterium's competence to make with any authority.
Which is why I don't think that Nostra Aetate 4 played any role in the DP at all.
My objection to the SSPX, aside from their disobedience, quasi-schismatic behavior (on display in this thread !!), and wrong ecclesiology is very simple:
A substantial percentage of their adherents reject the new Mass, even when celebrated according to the rubrics, as invalid. There's even, IIRC, an SSPX examination of conscience I've seen which identifies attending the new Mass as a sin to be confessed!
The proposition that the new Mass is intrinsically invalid (I'm speaking of Masses celebrated according to the rubrics, not ones full of invalidating liturgical abuses which are recognized as such by Rome) is a heresy against the dogma of the indefectibility of the Church. That SSPX & friends tap-dance around this heresy on a regular basis means that they are both quasi-schismatic and quasi-heretical.
Come back to the Catholic Church. If there isn't a parish near you that offers the EF Mass, see if you can get one started.
Jews deny the Holy Trinity, the Divinity of Christ, etc.
What are your thoughts on that matter?
Specifically, do Christians and Jews worship the same God?
So, having said that: the Tome of Damasus anathematizes all of those who reject the Trinity. The Council of Ephesus condemns all of those who reject the Nicene Creed.
Muslims reject the Nicene Creed and the Trinity. (They consider it blasphemous, in fact.)
Therefore, for the Vatican Council to assert that "Muslims worship the same god as Catholics," meaning "the same god in all his attributes and in every respect," not merely "they got some of the basics right" -- then they would be anathematizing themselves.
That is impossible (and of course there was no change in Catholic belief regarding the godhead at Vatican II), hence the premise -- that VC II asserted that Muslims worship the same god as Catholics in all his attributes and in every respect -- must be false.