What is the ruling on partnering with a Christian woman in a real estate office and giving her half of the financial income?

There is no objection to partnering with a non-Muslim, even though some scholars dislike partnering with those who do not refrain from the unlawful, such as the dissolute or the disbeliever. This is permissible as long as the field of work is lawful. There is no objection to agreeing on a 50% profit share, while observing the Shariah-compliant regulations for interacting with a non-mahram (definition) woman, such as avoiding unlawful seclusion and not speaking in a soft, alluring manner. One must treat her with honesty and without treachery, for Allah is the third of the two partners as long as one of them does not betray the other. It is not permissible to deceive, trick, or wrongfully consume the wealth of a non-belligerent disbeliever. A Muslim must showcase the virtues of their religion through their conduct and dealings.