The solution is to use git difftool. With the following config command, I can add a custom diff tool called idiff for Git to use:
git config --global difftool.idiff.cmd 'diff -i $LOCAL $REMOTE'
With this customization, I can see the case-insensitive comparison like so:
git difftool --tool idiff <other diff options> <Git references or files>
Eg.
git difftool -t idiff HEAD~1 -- my_schema.sql
Since git difftool prompts (for yes/no) every time before invoking the the tool, either use -y switch for difftool or add this config option to avoid the prompt:
git config --global difftool.prompt 0
UPDATE (2021/11/26): Here’s a consolidated configuration I use, that allows me to use git idiff command that behaves almost identical to how git diff behaves.
git config --global difftool.idiff.cmd 'diff --unified=3 --color=always --ignore-case $LOCAL $REMOTE | less --raw-control-chars'
git config --global difftool.prompt 0
git config --global alias.idiff 'difftool --tool idiff'