The build uses ccache if it's installed, but it only checks that ccache is installed on the host system. If ccache is not also installed within the chroot environments then you will see (a version of) the following error:

checking for gcc... /usr/bin/ccache gcc
checking whether the C compiler works... no
configure: error: in `/home/ehoover/src/proton/build/wine.win64':
configure: error: C compiler cannot create executables

You can work around this by running the following commands:

schroot --chroot steamrt_scout_beta_i386 -- sudo apt-get install ccache
schroot --chroot steamrt_scout_beta_amd64 -- sudo apt-get install ccache

The easiest way to deal with this is probably to check for the ccache binary existence in build_proton.sh, for example:

if [ "$($I386_WRAPPER ls $CCACHE)" = "" ]; then CCACHE=""; fi
if [ "$($AMD64_WRAPPER ls $CCACHE)" = "" ]; then CCACHE=""; fi