Is it permissible to download videos available on YouTube that are free of copyright, and then re-upload them and earn money from them, given that YouTube does not object to this?

The fundamental principle regarding copyrights and similar intellectual property rights is that they are protected for their owners, and it is not permissible to infringe upon them. The reference for determining what is copyrighted and what is not is common practice ('urf) and circumstantial evidence. If the evidence indicates that the videos are copyrighted, then it is not permissible to use them in a way that infringes upon copyright. However, if they are not copyrighted, then there is no harm in profiting from them. As for a specific website and distinguishing videos therein, this is not within our purview.