How do Christians approach the evangelization of individuals who have had profound spiritual experiences in other religions?

Spiritual experience and interpretation

As we can see in the Wikipedia article for religious experience, the same experience can be interpreted differently depending on the framework used, whether it is a religion or an academic discipline. Various philosophers, psychologists, anthropologists and religious study scholars have attempted to provide a taxonomy of this experience which then helps provide an interpretation of a person's spiritual experience:

• To an atheist psychologist like William James, all experience will be mere psychology (the premise of his classic 1902 book The Varieties of Religious Experience).
• To a new age spiritualist, all experience is bound to be interpreted in terms of psychic energy, past lives, higher self, etc.
• To a Platonic mystic, all experience represents the ascending awareness of the One.
• etc.

In Christianity, this task is usually the province of mystical theology or Christian spirituality, which provides a link between the raw experience and Christian theology, in order for the person to utilize the experience for his/her spiritual growth to thrive in his/her life of faith such as:

• to be closer to God
• to grow in love to others
• to be more aware of sins & Satan's temptation
• to have greater desire to follow Jesus
• etc.

Mapping non-Christian spiritual experience

In the context of Christian evangelization, the obvious approach is then to interpret the spiritual experience of the non-Christian individual in Christian terms, utilizing the taxonomy and interpretation provided by a Christian mystical / spirituality textbook.

Of course different denominations have different methods, building on centuries of the denomination's experience. Catholicism and Eastern Orthodox are particularly rich in this, having multiple mystical traditions to choose from. For example, a Jesuit missionary would use the wisdom of St. Ignatius of Loyola to first label the experience as either

• coming from God (even though previously interpreted in terms of another religion)
• coming from Satan, or
• coming from the individual (psychological or metaphysical)

He then leads the individual through an examen, discernment, and meditation in the context of an Ignatian retreat. That way, the Ignatian spiritual director could then provide a natural path for framing any positive element from the individual spiritual experience into an awareness of Jesus, which then becomes the building block for the individual's response to the gospel presentation.

Desired result of the Christian reinterpretation

In the process of mapping, interpreting, and building on the individual's spiritual experience, the hope is for the individual to see this experience as one or more of:

• A strong experience of God as ground of his being
• God's loving personal self-disclosure to him/her
• Jesus calling the person to Him, as in the hymn Softly and Tenderly Jesus is Calling
• etc.

so that the individual (with the guidance of a sensitive pastor / evangelist / Christian) will use that experience as a launching board for a Christian faith journey to heaven.

Why insist on Christian reinterpretation

Christianity's God is the creator of everything that exists, both visible and invisible. The invisible includes:

• all faculties of the soul (psychological, conscience, awareness of spiritual beings, psychic powers, etc.)
• the realm of spiritual beings (angels, demons, rulers & principalities, magic in nature, souls of people in purgatory, saints in "heaven", and of course God himself, etc.)

Since all is part of God's creation, Christianity has a say on how each soul faculty is good and how it can be corrupted. Christianity also has a say on proper communication and proper service provided by spiritual beings. Therefore, Christianity has a responsibility to map non-Christian interpretation of those things to the way Christianity view things, bringing them "under new management", so to speak.

Conclusion

Short answers to your 2 sub-questions:

How do Christians approach the evangelization of a person who has deep convictions about a different religion because of profound spiritual experiences they've had while following said religion?

Answer: Christianity has a place for anything genuinely from God, the task is to relabel the experience in Christian terms. Successful conversion needs to include the individual's willingness

• to focus only on elements of the experience that comes from God, and
• to let go any elements that Christianity labels demonic / irrelevant (example: foregoing magic, past life "experience", etc.)

How to argue against a strong conviction that comes from a profound spiritual experience someone has had in another religion?

Answer: I think it's pretty much established in the academia that spiritual experience does NOT provide its own interpretation, but the framework comes from OUTSIDE the experience. Therefore, if an argument against is needed, it is an argument for the non-Christian individual to let go of his/her previous interpretation in exchange for a Christian one. If the profound experience is Godly, there should be no issue. If it is demonic, then we should show how that experience is enslaving, not liberating.