Anyway, if Abraham was a Muslim because he was a man of "peace", he was certainly a Jew as a man of "praise" and certainly a Christian as a man of "anointing".

Are you familiar with The Apocalypse of Abraham? it's a manuscript dated after 70 AD (text must post-date 70 due to its knowledge of the destruction of the temple) and before 150 AD. The Apocalypse of Abraham belongs to a body of Abraham literature flourishing about the time of Christ. "The Book is essentially Jewish," wrote George H. Box, with "features... which suggest Essene origin." From the Essenes it passed, he suggested, to Ebionite circles ... and thence, in some form, found its way into Gnostic circles," though "Gnostic elements in our Book are not very pronounced." -- Dr. Hugh Nibley (Abraham in Egypt)

That in fact a book known as The Apocalypse of Abraham existed in his time is explicitly stated by Epiphanius where, in speaking of the Gnostic sect called “the Sethians,” he says they possessed a number of books “written in the name of great men,” seven in the name of Seth, and among others one “in the name of Abraham which they also declare to be an apocalypse,” and which is “full of all wickedness”.

So I don't think "Muslim" means what you think it means

Nothing wrong with a bit research into the subject. I enjoy studying and learning new things.