The Salvation Army is a charity that operates as an evangelical effort of Christians.
The Salvation Army is a church denomination, just as Methodist, Baptist, Presbyterian, Catholic, etc., that operates charity works.
You are 100% correct.
And they are pretty open-minded. No one is commenting on the fact that they'd already employed the man for 2 years. This proves they are not bigots.
He was asking to step up into a position more at the core of their mission, and they wanted specifically to know that he would represent their basic underlying interest....faith in Jesus Christ.
He failed to reassure them of that, and they didn't select him.