Alabama newspapers didn't pick up on any problem with his remarks, but national media (looking for SOMETHING to write about in a slow news week) turned it to possibly mean that he would only be responsive to Christians while in office. He has spent the rest of the week explaining and apologizing.
Are all "brothers and sisters"? As part of the human race, yes. But for believers in Christ, there is a familial link unknown to those who do not believe. The New Testament writers used such terms as fathers, mothers, brothers and sisters in writing to Christian believers, whether Jew or Gentile. And that non-believers are outside that family, we look no further than the Lord Jesus Himself, who referred to the faith-denying religious leaders as "children of the devil". They were part of a "family", but not His!
The fact is, true Christians do acknowledge, despite secondary doctrinal or denominational differences, that they are "brothers and sisters". Furthermore, the invitation is open to all to come into a relationship with the Lord Jesus and to receive Him as one's own Lord and Savior. This personal act has the added benefit of becoming a member of His family, and every believer is a part of that.
Governor Bentley seems to have smoothed all the ruffled feathers, for now. But he refuses to deny his own faith in the One who (exclusively) stated, "I am the way, the truth, and the life: no man cometh unto the Father, but by me." (John 14:6).