Shell set environment variables for command
The variables are set only in the current scope, to make them visible in a program that is called or after a source (e.g. . file) you need to export them.

Thus program_variables.config should be

export VARIABLE="value" 
export VARIABLE2="value2"


Then just run the executable,

This can all be in one script to run the executable

#!/bin/sh
export VARIABLE="value" 
export VARIABLE2="value2"
run_program


Save this file and make it executable.
Then just use the name os this file as the program