She is an assassin not a guardian,
She was a scribe and the role she takes at the end is guardian of the Sierra Madre.
and not BOS anymore either
Regardless she was Brotherhood before.
I dont think, her speech made it a little unclear on that point,... I think she left because of BOS stand on homosixual relationships, and didnt Veronica say she (Christine) had left the brotherhood because Elijah had broken up their relationship himself ?
No, Veronica says it ended but he never says Elijah make them brake off.
Christine says (well gestures) that Elijah make then brake off, the exact details are not given but my impression was Veronica was unaware of Elijah role in the end of their relationship, that also makes me suspect as the BOS due to how their membership is "keep in the family" takes a poor view at homosixual relationships but does not go father then that (as someone leaving the Brotherhood is even worst for them) but Elijah pulled some strings and then having Elijah going AWOL was just the last drop for Christine, I see no indication they made Christine leave the Brotherhood because Veronica is under the impression their relationship ended because of the Brotherhood views, no way in hell would Elijah being able to cover up the fact one of the scribes was thrown out, not to say Christine would be unaware of Elijah movements since he only became a outcast to the Brotherhood when he vanished during the battle of Helios One that was a somewhat recent event, before that he was a Brotherhood Elder.