Yes, on a 4wd both front and rear differentials need to have the same ratio (within a tiny bit of variation - a 4.10 and a 4.09 would work together). That is among the many reasons why I want to find something more modern for my rear axle - there aren't that many gear options for that ancient Eaton-style axle, and no limited slip options except for a Detroit Locker that hasn't been manufactured for 25 years.
Thanks to everyone for their suggestions on axles that might work for my project.