On RHEL systems, the /etc/rc.d/init.d/functions script is intended to provide similar to what you want. If you source that at the top of your init script, all of it’s functions become available.
The specific function provided to help with this is daemon. If you are intending to use it to start a daemon-like program, a simple usage would be:
daemon --user=username command
If that is too heavy-handed for what you need, there is runuser (see man runuser for full info; some versions may need -u prior to the username):
/sbin/runuser username -s /bin/bash -c "command(s) to run as user username"