Is it permissible for a government employee to take raw materials from their workplace for use in their private project, in exchange for compensating the government entity with other items of the same value, and is there any religious doubt in that?

You are not permitted to take materials from your government department and replace them with other materials of similar value, for two reasons: First, the competent authorities have not authorized you to sell these materials. Second, even if they were to authorize you, you are not allowed to sell them to yourself, because an agent appointed for selling is not allowed to sell to himself. This is the view of the Shafi'is and Hanbalis, and one opinion within the Hanafi school. However, the Hanafis and Malikis permit it if the principal authorizes it.