What i have seen with rip auth, is that it depends in what order you set the commands for rip auth.
First you have to enter the key chain “key chain RIP” “…”
After you have to enter first on the interface “ip rip authentication key-chain RIP”
And then you can enter the encryption mode “ip rip authentication mode md5″
If you change any of this in order, it might not work and you have to re-apply your configs. Btw. not many are using RIP these days, but better to know for the lab, cause it’s still there.
Check always with “debug ip rip”, if authentication works!