Came across investigating trybot failures ( https://codereview.chromium.org/2755963002/ ; well even without what I'm suggesting here, it should not fail. ). 

In https://codereview.chromium.org/2041413004.  the following was done:

Normalize fields before comparison to fold case, remove diacritics,
      remove punctuation and collapse or remove whitespace.


 std::unique_ptr<icu::Transliterator> transliterator(
      icu::Transliterator::createInstance(
          "NFD; [:Nonspacing Mark:] Remove; Lower; NFC", UTRANS_FORWARD,
          status));

However, "NFD; [:Nonspacing Mark:] Remove; Lower; NFC" is not necessary because icu Collator is already used (can be used) to compare strings with strength set to PRIMARY (in some locales, it might not be PRIMARY, though). Normalization is also taken care of by ICU collator. 
PRIMARY strength means both diacrtics and case differences are ignored.


In the following code snippet, strength can be set to PRIMARY explicitly for the 1st ctor to avoid any locale difference. 

----------
CaseInsensitiveCompare::CaseInsensitiveCompare()
    : CaseInsensitiveCompare(icu::Locale::getDefault()) {}

CaseInsensitiveCompare::CaseInsensitiveCompare(const icu::Locale& locale)
    : collator_(GetCollatorForLocale(locale)) {
  if (collator_)
    collator_->setStrength(icu::Collator::PRIMARY);
}
----------------