Essentially Christian "values" include the belief that human nature is inherently sinful (because of the Fall), the belief that a universal battle between good evil exists and is ongoing, and the belief that humans must rely on the redemption of Jesus Christ (because of His work on the cross) in order to be "good" or to obtain perfection (in Heaven).
That being said, many of Shakespeare's plays reflect the universal battle between good and evil, but Othello more than his other plays contains many references to the Garden of Eden and the struggle between the serpent (Iago) and the "happy" couple (in this case Othello and Desdemona instead of Adam and Eve). What I find interesting about Shakespeare's portrayal of the serpent tempting humans is that Iago is constantly suggesting ideas and doubts to Othello rather than the Edenic version of the serpent tempting the woman first. Perhaps Shakespeare was trying to demonstrate that males are just as susceptible to being manipulated as women are.
In regards to historical relevance, Shakespeare was not a pioneer in using Christian themes or allusions to discuss universal truths or ideas. Because the Church maintained such power during the playwright's time period and far beyond it, writers were schooled in "Christian" values and often used them in their works because not only were they easily recognized by their audience, but the use of them pleased wealthy patrons such as Queen Elizabeth and King James.