Grammaticality – Why Is This Sentence Ungrammatical: ‘He Is the Kind of Person Who, if He Had Lived …’

First, as others have pointed out in the comments, the sentence uses "who" when it should use "whom." Even native speakers fail to correctly distinguish between "who" and "whom". It is common for "who" to be used in all cases, but this is not recommended in formal speech or writing. I have made that correction throughout the rest of the answer. However, there is a larger issue in the sentence, which I believe is the intended focus in the original source.

I think the issue becomes clearer if you omit the nonessential clause "if he had lived in the 19th century".

He is the kind of person whom people would not have been able to categorise him.

One could write "People would not have been able to categorise him." as a complete sentence, or one could write "whom people would not have been able to categorise" as a relative clause describing "person". However, the example sentence combines the two, beginning as a relative clause and ending with another pronoun "him". In this sentence "whom" is already the object of "to categorise".

We can remove "him" and reintroduce the nonessential clause to get the correct sentence:

He is the kind of person whom, if he had lived in the 19th century, people would not have been able to categorise.

The nonessential clause interrupts the flow of the sentence, which can make it more likely to miss mistakes like this one both in reading and in writing. While the sentence is now correct, an even better sentence might be:

He is the kind of person whom people would not have been able to categorise, had he lived in the 19th century.