While I feel for this Pastor I don’t think he has much of a legal case unless he has a written employment contract and can point to a specific breach.
He doesn't have any case. SCOTUS made it quite clear in the Hosanna Tabor case that churches and church organizations can make employment decisions concerning their leadership on any grounds they choose, even if those grounds could would be a violation of employment and non-discrimination law in other settings. The government just cannot get into the business of determining who can be a minister in a church.
In this case an employee of the church made public statements through his book that apparently contradicted or called into question the teachings of the church which employed him. That certainly seems to be sufficient grounds for termination.
As far as expelling him from the church, any church has the right to determine who may be a member. There is a right to worship as you choose in this country, but there is no right to attend a specific church even over the objections of that church...