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There are not much to say other than the usual missing argument null check:

It is valid to write the following:

 string test = null;
 test.RemoveDuplicateChars();

and RemoveDuplicateChars will be called with a null for the this argument text. Therefore you'll have to test for null:

public static string RemoveDuplicateChars(
 this string text, Func<string, string> normalizer = null)
{
 if (text == null)
 return text;
 ...

or throw an exception...

The default initialization of normalizer could be a little less verbose:

 normalizer = normalizer ?? ((x) => x.Normalize());

A minor detail: Angstrom and Å: is also represented by \u00C5, which your code interprets as equal to Angstrom, but MS Word interprets them as different when using its Find-function?