Mumu was not without a place to stay in the Seaside District, but she didn't go to the headquarters of the New Church of Eternal Life immediately.
She and Xia Yubing hadn't revealed their true identities at the New Church of Eternal Life, covering themselves with aliases. This was not only a precaution against Max but also made it easier to cut ties and escape at any moment.
Legends are just legends, they can't be officially recognized, right?
Moreover, Max couldn't be of much help. Others might not know, but how could Mumu herself not know that the current New Church of Eternal Life was just a shell company, with core members from top to bottom not doing their proper jobs, some living off incense offerings and others embezzling money.
If really necessary, she could call Xia Yubing for help, but that wasn't needed yet.