Thanks @Nathan_Stone1!
This seems to be an issue with the specific fasttree package that was installed on the system.
The following should generally work. This will uninstall the fasttree package that was installed from the biocore channel, and then install the package from the bioconda channel. It then re-installs q2-phylogeny, as that gets uninstalled with fasttree.
conda remove fasttree
conda install -c bioconda fasttree
conda install -c qiime2 q2-phylogeny
These commands were tested on a Linux system and solved the problem (incidentally, this is the same Linux system that @Nathan_Stone1 initially encountered the problem on, as we’re at the same institution).