The shell startup scripts are kinda funky.  When starting a
non-interactive login shell, ~/.bashrc is sourced twice, once from
~/.bash_profile and again as $BASH_ENV. See bash man page.  (Also bad
because it uneccessarily causes ~/.bashrc to run in non-interactive,
non-login shells, when none is needed.)

Now, bash's startup script needs are confusingly awkward, but here's one
way to handle it: Put everything in a bashrc file in two sections, one
for exported stuff, one for non-exported stuff, each protected by it's
own environmental variable such that when the variables are undefined,
only the non-exported stuff is used (like a normal bashrc file). Then
source the file from a profile file with variables set so both parts are
used.  (If someone wants to use ENV or BASH_ENV, they can have the
profile file cause only the first part of the bashrc file to be used
from the profile file.)