Judaism was an ancient and long established religion in the Levant by the time the Roman Republic came into contact with them. They had been under the suzerainty of the Seleucid Greeks for about a hundred years, and had a culture that deeply valued learning, literacy and the law, so they weren't barbarians by any definition. The Romans respected their culture as ancient, and being on par with other cultures in the region (at least until the Judeans started rebelling too frequently).
I'm not an expert, but I don't think that's completely true. The Romans conquered Greece and then Greek culture conquered Rome. I'm not aware that they viewed the Persians, Egyptians or Carthaginians as barbarian either.
Unless barbarian strictly means foreign, rather than uncivilized.
I wasn't able to find a super authoritative source, but here's a PBS [1] article that lays out the basics - the Romans allowed the Jews to worship their own deity and follow their own practices, and Pompey, Caesar and Augustus all maintained that protection into the early imperial era. They were treated like clients, rather than being subjugated, until the rebellions.
Wouldn't the people who wrote the old testament have been considered barbarians by the Romans?