I have this issue with my legs - had a difference prior to hip replacement, hip revision was complicated, resulting in a 3rd surgery, which unfortunately increased the difference to 1/2". The ortho was very apologetic, but to get my hip to not dislocate repeatedly, it was necessary.
That was 11 years ago, and I have learned to live with it (am grateful the difference is not greater - my brother has a leg difference of over 1")

So, I wear a 1/4" lift in the shoe of my short leg, or when I wear my orthotics, that one is built up an additional 1/4" and no walking barefoot or I get sore.
Sue