It certainly is not an anachronism.
I may be wrong (and I’m writing mostly from memory here, hopefully without too many inaccuracies

), but I think it is, indeed, an anachronism.
Within the Church, the condemnation of modernism followed the development of Liberal Catholicism, which is a 19th century-early 20th century phenomenon. It is deeply linked to the changes brought about to the Western world by modernity and industrialisation, and the correlated emphasis on the notion of subjectivity and its consequences, such as the multiplying of “truths” which accompanied the multiplying of viewpoints – the whole “truth is relative” idea.
I am weary of projecting such a concept on an individual who lived 2 millennia ago, in a culture which had a different view of truth.
It is the false belief that the truth can be moderated to suit the moment. That neatly sums Pilate’s outlook.
To me, saying this assumes two things: that one knows what Pilate’s outlook was (I, for one, do not, and I don’t think the text is particularly clear on that), and that the false belief that the truth can be moderated to suit the moment was actually a thing in 1st century Roman thought. I am not so sure of that, because I am not sure it would have entertained the notion that truth was relative.
Schools of thought like stoicism, which had some prominent representatives in the 1st century, had a relationship to truth which could maybe have been said to be subjective. But, if I remember correctly, it is only in the sense that it was dependent on the thinking subject’s ability to grasp correctly a given reality (which may or may not have been the background for Pilate’s question). In other words, truth was considered as objective but not necessarily within reach, in which case one had to work at best with approximations, like gradations on a scale running from “false” to “true”.
This relationship to truth was accompanied by the fundamental postulate that virtue – objective virtue – was the chief good towards which all must strive. If you did not strive for virtue and allowed your passions to govern your decisions, then you were nothing more, to quote Zeno’s famous words, than a dog tied to a cart, forced to follow wherever the cart led you.
This was an outlook which had not, as modernity did, emptied both the notion of virtue and the notion of truth of their objectivity.
Pope St Pius X defined modernism as “the synthesis of ALL heresy.”
That does not mean that modernism was, from the beginning, coexistent with every heresy in the Church’s history. It is, precisely, a synthesis.