Ended up with setting the path to DealiiCutElements when I run cmake:
$ cmake -DCUTFEM_DIR=~/git/path/to/dealiicutelements/install ..
$ make -j4
Get the Deal.II docker image from https://hub.docker.com/r/dealii/dealii/
$ docker pull dealii/dealii
Run an interactive shell in the container with this project as a volume in the container
$ docker run -itv ~/path/to/microbubble:/home/dealii/microbubble
dealii/dealii:<tag>
If the project have already been compiled on the "outside" it may be necessary to delete all Cmake output before running the container.
Inside the container, compile by running
$ cd microbubble/
$ cmake .
$ make