Unless you are a dualist, the question seems moot. Only a dualist would classify things as physical/not-physical.

To an anti-realist, information is not physical because NOTHING IS.

To a physicalist, information is physical because EVERYTHING IS.

Is the implication then that we are all actually dualists? Or is something else meant by "physical" in this context?

And then there is the question of the meaning of the term "information". I would argue that a poor choice has been made by physicists in adopting the word "information" to describe quantum states. Like using "real" and "imaginary" to describe numbers in math, the term "information" has too strong of a colloquial usage (i.e., tied to the mental activity of interpreting symbols - or of a mind choosing to assign a meaning to an observed thing). Back at the beginning of the discussion, Bitter Crank asked if DNA is information. Well, DNA is a complex physical arrangement of genes that a particular system can react to, but calling it "information" might imply that the system is conscious and assigns meaning to the DNA. So the question of whether information is physical or not might hinge on whether you believe consciousness is physical or not.