The term "born again" only appears in the reporter's or editor's title for the article. The only requirement is that they want someone that belongs to a Christian church. Are Catholics and Orthodox really excluded, or are they simply saying any non-Christian need not apply? I'm assuming they would refuse Mormons, Jehova Witnesses, and others that would be viewed as cults or sects. I'm also sure Jews, Hindus and Muslims, etc. need not apply. I only see and read what they have in the job notice. I'm not reading into it what I want it to say.
Never trust a reporter. They all put their spin into a story. Real journalism is dead. I have no doubt the writer is a liberal that not only had to go after "born again" Christians ( a real redundant term if there ever was one, and one of the liberals favorite bogeymen ), but take a shot at Michele Bauchman too. You will notice no one from the church was asked about who they were looking for and what does or doesn't qualify to clarify what they are looking for. Be discriminating readers. The author, and paper, are looking to attack a conservative church and candidate running for president.
This is still the USA, or what's left of it, where we have freedom of association. The church is free to set the qualifications however they want whether you or I or anyone else agrees or disagrees with them.