Don't read it into it more than it actually says. It never says that Catholics and Muslims "worship the same God." It especially never says that if, by "worship the same God," you mean "understand the God they worship the same way".
The passage you're getting that idea from (I think) is this:
together with us they adore the one, merciful God, mankind's judge on the last day.
This is factually correct, in that Muslims identify the God they worship as (a) one, (b) merciful, and (c) mankind's judge on the last day. Christians also identify the God they worship as having those same attributes. (Not only those attributes, of course, but those attributes.)
As I've previously explained, even if you suppose this passage from Vatican II's Nostra Aetate is an infallible dogmatic statement (which I think is most unlikely, but just for the sake of argument), the Catholic Church does not claim to be able to make infallible statements about other religions, so she would be incapable of infallibly teaching that "Muslims worship the same God" even if she wanted to.
(As an aside, "not infallible" doesn't mean "Catholics can safely ignore this". It does, however, mean that the teaching is not set in stone for all time.)
All this passage is doing is attempting to be diplomatic to the Muslims, saying "look, we have this much in common with you". That means the Muslims are closer to Christianity than other non-Christian, non-Jewish groups.
(Another aside: people who don't know the context of this remark sometimes think that "in the first place amongst whom" puts the Muslims above everyone else. The passage actually occurs after an extensive discussion on non-Catholic Christians and then another one on Jews. I think it's hard to dispute that, after Judaism, Islam is the (major world) religion closest to Christianity. Some scholars even argue that Islam should best be understood (theologically if not historically) as a heresy from Christianity.