FairMormon is a non-profit organization dedicated to providing well-documented answers to criticisms of the doctrine, practice, and history of The Church of Jesus Christ of Latter-day Saints.
Question: How would a statement that "God is a spirit" be interpreted in ancient Judasism?
Question: How would a statement that "God is a spirit" be interpreted in ancient Judaism?
The statement that "God is a spirit" does not mean that he has no body - it means that he is the source of life-giving power and energy
Christopher Stead of the Cambridge Divinity School (another non-Mormon scholar) explains how a statement that God is spirit would have been interpreted within ancient Judaism:
By saying that God is spiritual, we do not mean that he has no body … but rather that he is the source of a mysterious life-giving power and energy that animates the human body, and himself possesses this energy in the fullest measure. 
It may be that Joseph Smith, by revelation, had something like this in mind when he wrote that the Father is "a personage of spirit."
- Christopher Stead, Philosophy in Christian Antiquity (Cambridge: Cambridge University Press, 1994), 98.