Currently str.replace() has 3 arguments: old, new and count.
This issue suggests the new addition of another argument called case_insensitive (type bool, defaulted to False) which determines whether to ignore case when replacing said text or not.

Currently we have to use regex or logic (see https://stackoverflow.com/questions/919056/case-insensitive-replace), but it would just be a nice QoL feature to have a case_insensitive kwarg.

I don't think this should be done.  

If case doesn't matter at all, the input can be casefolded before the replacement:

  s.casefold().replace('hippo', 'giraffe').  

If it can't be casefolded in advance because the case actually matters, then ​it doesn't make sense to mix a case-insensitive search step with a case-sensitive replacement.

Presumably if case matters at all in the original string, then the new text would need to match the case of the old text.  With the example in the selected StackOverflow answer, we get undesirable output for most of the case variants:

 ​strings = [
    ​'I WANT A HIPPO FOR MY BIRTHDAY!',  # lowercase giraffe doesn't fit
    ​'I want a hippo for my birthday.',  # only makes sense when the case matches
    ​'I Want A Hippo for My Birthday',   # lowercase giraffe doesn't fit
    ​'I want a hIPpo for my birthday',   # desired outcome unknown
 ​]
 ​for s in strings:
     ​print(s.replace('hippo', 'giraffe', case_insensitive=True)

ISTM that every answer in the StackOverflow entry has only a toy examples and wouldn't make sense for real text where case is retained everywhere except for the substitutions.

I agree with Raymond that this should be rejected.

I concur with Raymond and Eric.

Note that in general case the problem is more complex that you may expect. First, some characters can match two characters (e.g. 'ß' matches 'SS'), and therefore indexes of characters are different in different cases. Second, you may want to take to account Unicode normalization, so 'й' will match 'й' (the former is a single character, the latter is two characters 'и'+'\u0306').

The re module will not help with solving the first problem. You should use the third-party regex package. For the second problem you can use unicodedata.normalize(),