I don't think you can be classically liberal and also not be in favour of free speech.
Which aspects of free speech is it you consider The Guardian to oppose and classical liberal thinkers to support?
I would say one area of vulnerability would be the request that mis/disinformation (broadly defined as stuff they disagree with) be suppressed.
Where have they argued for suppression of "disinformation" "broadly defined as stuff they disagree with" should "be suppressed"?
That further is actually published as the view of the paper as opposed to opinion pieces, that often are "stuff they disagree with" yet still are happy to publish.
The closest I've come to seeing an official statement arguing for some degree of regulation have been mild and vague. Even one stating that the cost of fake campaign videos is real, and pointing out genuine concern over implications to democracy, only called for "paying attention" and "developing suitable responses".
My impression is that The Guardian is about as firm as a wet blanket when it comes to taking a stance against movements leveraging misinformation.
The classical liberals support regulating speech on the basis of the harm principle. The quibbling comes down to what you count as "harm".