Paolo, you don't disagree with me, you disagree with scholars working in this field.
There is no ancient tradition that says Thierry was a Jewish prince. That is a modern theory developed by one scholar, then immediately rejected by every other scholar.
In 1972 Prof. Arthur Zuckerman wrote a book (A Jewish Princedom in Feudal France, 768-900). In one part of the book he argued that Makhir was the same person as Natronai ben Habibi, so Makhir was a Jewish prince and a descendant of David. Then he argued that Makhir was the man called Maghario, count of Narbonne, and that Maghario was the same person as the fictional Thierry, count of Narbone, and Thierry was the same person as Theuderic, the the real life father of William, count of Toulouse, whose descendants we know.
There are many problems with this chain of identifications. The biggest problem is that it's all speculative.
Nat Taylor published an article in The American Genealogist (1997) giving his detailed objections:
http://www.nltaylor.net/pdfs/a_Makhir.pdf
Maybe someone will find new evidence, but for now it's just a modern theory that didn't work out.