First, determine if the issue still exists.

This issue does still exist.

Currently working on issue.

Karthik and I met to look at the File Chooser and it turns out that the duplicate file extension problem does not occur on his machine. We are both running Windows 10 Home edition.
I have multiple versions of IGB installed on my computer. It sounds like Irvin had been having a similar problem where having multiple version installed causes some code changes to not be reflected.
I have uninstalled all versions of IGB from my computer, but no luck getting it to work yet.

Tested on 9.1.6 release and 9.1.8 Master.
Issue persists on Windows 10 Home 10.0.19041 Build 19041.

I installed IGB on a computer which never had IGB installed on it before;
Like Karthik's computer, the duplicate file extensions were not present.

I think the problem I need to address now is how to completely clean all traces of IGB off of a computer.
I suspect this sort of thing is happening with more than just this issue.

We have been unable to create a "Naïve system" on my machine, and the duplication issue persists.
Karthik and the new computer I mentioned above are both running in Windows 10 and do not have the duplicate file extensions.
Dr. Freese is running MacOS and does not see the duplicate file extensions either.

Credit to Karthik for identifying a possible problem:
The source of the file-extension may have changed from the older version to newer version of IGB, so the extension filter is not catching it to remove the duplicate.
The file-extensions and file-type could be located in different files and are getting combined, resulting in two extensions being displayed.
Newer versions of IGB could be looking at only one source, so there is no duplication problem.
My computer, because it has files from past versions, is getting the file type returned to it from multiple sources and not just the recently installed source.

To create a Naïve system:
Reset preferences to default by: Launching IGB > Preferences > Other Options > Reset Preferences to Default
Delete the IGB folder in AppData located at C:\Users\<user>\AppData\Roaming\IGB (sometimes the AppData folder is "hidden", Go to the View tab in File Explorer and check the Hidden Items checkbox)
Go to the IGB installation folder (defaults to C:\Program Files\IGB ) and run the uninstall.exe application there.
Now when you reinstall IGB, it should act as if IGB has never been installed.

We were considering having additional Windows user's try and reproduce the bug since it is not consistently reproducible now.
But since the problem does not seem to occur with new users based on my testing;
and it looks like fixing this aesthetic problem would require a major deep dive and change to the code -

[~aloraine], would you like this problem to be further investigated?

Thank you for the clear explanation Logan Weidenhammer.
Marking this issue as complete.