You can use the skip-worktree bit. Turn it on with:
git update-index --skip-worktree <file>
After that, git will never stage local changes for <file> and will fail (loudly) if git itself has to write to <file> (say, in a merge or a checkout).
If you ever want to stage a future change, you can turn it off, stage the new change, and then turn it back on:
git update-index --no-skip-worktree <file>
git add -p <file>
git update-index --skip-worktree <file>
While not perfect, this might be good enough. It will be up to you to notice that <file> has unstaged changes, since git will no longer tell you that
Note: My original suggestion was to use assume-unchanged. As explained in Git – Difference Between ‘assume-unchanged’ and ‘skip-worktree’, it is really skip-worktree that you want. In particular, assume-unchanged is a promise to Git that you won’t change the file, and if you violate that promise Git is allowed to erase your changes or commit them! In contrast, Git will not erase or commit your skip-worktree changes.