As the fenics project is an open source project, it is dependent on people maintaining instructions. As no of the main developers has limited experience with conda, it has not been prioritized.
Any contributions to the conda packages are welcome.
@dparsons has been kind and maintained the fenics apt-packages.
I would like to note that mshr is no longer maintained, it is now recommended to use external meshing software, see: How i can make geometry and mesh in my program? - #2 by dokken for a list of suggested mesh generators.