What is the ruling on placing a cross image in the background of da'wah (preaching) videos when speaking about Christianity, and is it permissible to publish them despite the presence of this image?

A cross should not be displayed with the intention of condemning its adherents or clarifying their situation, as this goes against the prophetic guidance. The Prophet, peace and blessings be upon him, used to nullify anything that contained crosses. Moreover, displaying a cross is not the only means of condemnation, and the original principle is to nullify and remove the cross. As for publishing videos that include such content, it is preferable to avoid it unless there is a significant benefit that cannot be achieved otherwise.