If my friend openly disagrees with Church doctrines, should she be teaching RCIA?
The short answer
No. She may be caring and well-intentioned, but she is not qualified to teach. Church documents require catechists to hand on Christ's teaching, not their own opinions, and say there can be no teachers of the faith except convinced and faithful disciples of Christ and his Church.
Not qualified
Your friend is probably a caring, well-meaning person, but she is not qualified to teach the faith.
Catechesi Tradendae
Show your pastor Catechesi Tradendae: every catechist must strive to pass on, by teaching and example, the teaching and life of Jesus — not draw attention to his own opinions, and above all not present his personal views as if they were Christ's teaching. Every catechist should be able to say with Jesus that his teaching is not his own but the Father's.
The General Directory for Catechesis
It states that there cannot be teachers of the faith other than those who are convinced and faithful disciples of Christ and his Church.