Generally speaking, employment in Ohio is "at will" which means that either party may terminate the relationship at any time. The only limitations on that doctrine is that an employer cannot terminate an employment based on certain discrimination categories, race, religion, gender, pregnancy, age, etc.
However, faith-based organizations are often exempted from such prohibitions to the extent that they present a conflict with their religious teachings.
Even when an employer's stated reason for termination is untrue, that does not entitle the employee to sue for their job back. That is not what we mean in the law by wrongful termination. We mean that there's either a violation of state or federal discrimination statutes or some other public policy.
I'll leave it to the theologians to determine whether one could ever prove themselves "Christian enough." However, the answer to your question is that while what occurred may not be fair, moral, just, or ethical, it is legal.