Q. Is God real or just an idea?
A. Your actual question is longer than this. You say you are writing a book about how different religions envisage God. You say that some religions personalise or personify God whilst others regard Him as an intellectual abstraction. You ask what is the view of Judaism. My answer is that there is no one answer.
The medieval hymn Anim Z’mirot, which most congregations sing every Shabbat, says Himshilucha b’rov chezyonot; hinn’cha echad b’chol dimyonot, “They represented You in many ways, yet You are one in all the imagery”.
Some thought of God as a cosmic grandfather, others as a guarantor of ethics. Within Judaism the intellectual analysis of Maimonides and the emotional approach of Chassidism are both able to be accommodated. But there is a problem if one has a view with too much imagery, or too little. With too much imagery God can lose His grandeur and transcendence; with too little He is no longer a Being to whom one can relate.
Louis Jacobs has written, “The ascription of any kind of corporeality to God has in Judaism long been considered a major heresy. But the line must be drawn somewhere. God must not be refined out of existence”.