Why does updating Oh My Zsh give me an error about rebasing with unstaged changes?

You made a changes to the config files probably. Go to your oh-my-zsh directory and type in git status.

Results for me (i've changed one of the themes):

╭─ jane  ~
╰─ λ cd .oh-my-zsh                                                      1:57:10
╭─ jane  ~/.oh-my-zsh  ‹master*›
╰─ λ git status                                                         1:57:17
On branch master
Your branch is up-to-date with 'origin/master'.
Changes not staged for commit:
  (use "git add <file>..." to update what will be committed)
  (use "git checkout -- <file>..." to discard changes in working directory)

        modified:   themes/bira.zsh-theme

no changes added to commit (use "git add" and/or "git commit -a")

You will see that some files have been modified.

You can type in git stash to temporarily get rid of those changes, and attempt updating again.