Appending .patch or .diff to a GitHub pull request URL returns the raw patch or unified diff for the entire PR, without any UI around it.
https://github.com/org/repo/pull/123.patch
https://github.com/org/repo/pull/123.diff
.patch gives a format compatible with git am, so you can apply someone else's PR locally without checking out their branch:
curl -sL https://github.com/org/repo/pull/123.patch | git am
.diff is a standard unified diff, useful for piping into patch or reviewing programmatically. Both work on public repos without authentication.