Okay, so following your train of thought, the Jews do not believe in Abraham God.
But Paul says that the Jews have a zeal for God, they just lack knowledge.
Lumen gentium is about Christ as the light to the gentiles, the Nations.
At first it talks about how that light of Christ is most visible in the Catholic Church, then a bit less visible in non-catholic Christian groups.
Then they go on to talk about Jews, Muslims, and those who worship the unknown God. I think they are saying that each has a decreasing amount of light, of Revelation about God.
This line of thinking is not found just in Catholics. Many Protestants think the same thing, though they reverse the role of protestant and Catholic, with Protestant having the most light.
One of the big questions is what happens to people who have never heard the gospel or the name of Jesus. Are they condemned to eternity without God, or is it possible for them to go to heaven.
Here's a website with a lot of details
https://www.thegospelcoalition.org/article/what-happens-to-those-who-never-hear-gospel/
That particular website says that people who have never heard the gospel are condemned to eternity apart from God, I think that's what they say.
But not everyone thinks that, many Protestants don't think that.
So, do Muslims worship Abraham God? Well, as I talked about above, the answer a person gives will be related to how a person answers the question
do the Jews worship Abraham God?
If you look through the many posts earlier, I think you'll see that people other than myself have also said that the Jews worship Abraham God, in so many words. I believe you also said that the Jews worship Abraham God earlier, though I could be wrong about that. And of course Paul seems to indicate that the Jews worship Abraham God.
So in the same sense that the Jews worship Abraham God, the Muslims also worship Abraham God. They just have even less knowledge about God than the Jews.