Bash `-e` does not propagate to called scripts, but does to functions.

bash_caller

 #!/bin/bash

source ./bash_fn
set -e

./bash_script
bash_fn

bash_fn

#!/bin/bash

bash_fn() {
  echo "function: Before failing command"
  false
  echo "function: After failing command"
}

bash_script

  echo "script: Before failing command"
  false
  echo "script: After failing command"

Output:

$ ./bash_caller
script: Before failing command
script: After failing command
function: Before failing command

When you run a shell script, it's in a child process. Bash functions run in the same process as their caller.