I don't see any answer documenting how to work around this problem with cooperating processes. A common pattern with things like ssh-agent is to have the child process print an expression which the parent can eval.
bash$ eval $(shh-agent)
For example, ssh-agent has options to select Csh or Bourne-compatible output syntax.
bash$ ssh-agent
SSH2_AUTH_SOCK=/tmp/ssh-era/ssh2-10690-agent; export SSH2_AUTH_SOCK;
SSH2_AGENT_PID=10691; export SSH2_AGENT_PID;
echo Agent pid 10691;
(This causes the agent to start running, but doesn't allow you to actually use it, unless you now copy-paste this output to your shell prompt.) Compare:
bash$ ssh-agent -c
setenv SSH2_AUTH_SOCK /tmp/ssh-era/ssh2-10751-agent;
setenv SSH2_AGENT_PID 10752;
echo Agent pid 10752;
(As you can see, csh and tcsh uses setenv to set varibles.)
Your own program can do this, too.
bash$ foo=$(makefoo)
Your makefoo script would simply calculate and print the value, and let the caller do whatever they want with it -- assigning it to a variable is a common use case, but probably not something you want to hard-code into the tool which produces the value.