Is it permissible to enter the lavatory for someone carrying money with a Quranic verse and "صدق الله العظيم" (Allah the Almighty has spoken the truth) on it, and fears its theft if left outside, or for someone carrying a Quranic tape on which only the names of the surahs are written?

The majority of scholars dislike entering the bathroom with dirhams that have the remembrance of Allah or something from the Quran on them, unless they are covered. This is one of the narrations from Imam Ahmad. Jurists have explicitly stated the dislike of entering the lavatory with anything containing Quranic verses or remembrance that is not covered. As for carrying tapes that contain chapters from the Quran, there is no harm in entering the bathroom with them due to the absence of visible letters on them.