Can anyone help me with a javascript regular expression that I can use to compare strings that are the same, taking into acccount their non-Umlaut-ed versions.
Regex isn't better technology to solve this problem.
You should consider to create a dictionary to store your Umlaut character as key and non-Umlaut as value; Then you can to iterate over yourdictionary, check if it exists on your string and take appropriate action.