Rigid is not a good adjective to describe God. End.of.Story. The word rigid has negative connotations. Stick to describing God the way that the Church and the Scriptures describe Him.
The synonyms for rigid include stiff, hard, firm, inflexible, unbending, unyielding, inelastic. None of these describe God, unless you worship a harsh, unyielding old man in the sky who takes delight in punishing his creatures.
God is eternal and unchanging, an anchor in the storms, a firm foundation, who delights in mercy and gives good gifts to His children, who bends His ear to hear our prayers and is swift to rescue us.
Not rigid, unbending, inflexible.
Loving, Just, and Merciful.