It was definitely democratic. Every office except senator was decided by majority vote with universal male suffrage. And even Senators were de-facto elected, since elevation to the Senate was automatic upon the completion of a term in an elected office. Sure, Rome began as an Oligarchic Republic, but after the secession of the plebs in 494 BC 12 years later, it was solidly Democratic.
Think about it, if Rome wasn't a democracy, then why did the Populares exist at all? In an oligarchy, wouldn't a political party that panders to the masses be utterly powerless?
While Romans didn't call what they had liberalism, they definitely practiced a liberal society. People were free to speak their minds, travel as they wished, and speak for or against people in power however they wanted (see: Catullus and the invention of slam poetry).
All of these freedoms were locked down tight the moment Augustus came to power. People were okay with it, because having your speech, movement, and life trajectory restricted is better than being dead in a civil war, but Roman society under the Empire was way less free than Roman society under the Republic.