I want to perform a script on any number of files that do not have a .done suffix. In this case, my files have some values that I want to source and pass to a script.

My script looks something like this
How do I
1) source files that don't have a .done suffix
2) repeatedly perform /home/username/script_to_call on each file

Note that script_to_call is meant to only take in one file's values at a time (not all files' values at once). I want to perform script_to_call once for each file that does not have the .done suffix, essentially looping through all the sourced files.

Welcome. That's rather a sparse script. :/

One way to approach the task you describe would involve the find utility. See "man find" and scroll down to the -not, -name, and -print options. Then when you have it showing the results you would like, try adding in the -exec option.

Finding Files > Name > Base Name Patterns
Finding Files > Combining Primaries With Operators
Actions > Run Commands > Single File
@Turbocapitalist beat me to it.

Thank you! Does this method source the files in the same way source does?

Also, I need to pass these sourced values to script_to_call with flags like , where in this scheme do I implement that?

No, it doesn't. I'm afraid I misunderstood what you wanted. You should write a wrapper script, pass a file name as parameter to it, source this file from inside it, then call script_to_call with prepared flags and parameters. This wrapper_script is what you're calling in the find command:
Alternatively, you may try invoking sh -c in the -execdir action of find:

An alternative to find is a for loop over all files, and in the loop skip the unwanted ones