I think the main problem would have been an incredibly small nonviable gene pool.
You said Israelites so I'll take it you're starting with Jacob (Israel) as the cut off point.
Abraham married his half-sister, Sarah.
Isaac married his parent's great-niece Rebecca.
Jacob married his first cousins Rachel and Leah and took two concubines of unknown parentage. His brother Esau married a grand-daughter of Abraham and a number of pagan wives.
Abraham also fathered a son, Ishmael, from a pagan concubine and later took a second wife who also gave him a number of sons.
Ishmael married a pagan too and fathered twelve sons and unknown number of daughters.
You're then left with a Jewish nation descending entirely from Jacob's twelve sons and sole daughter and whatever spouses they can draft from their kinfolk descended from Ishmael, Esau and Abraham's other sons, who I would assume would also be faithful to YHWH.
From then on the level of in-breeding would be more than even Crufts could ever bare
