Derek Birdsall stated in his book "Notes on Book Design" that It should not be an arbitrary decision, "the suitability of type design to the subject of the book is less important than the nature of it's text"

what the meaning of "nature of it's text"?

There are no official standards for design of commercial books. There are excellent books on book design such as Book Typography: A Designer's Manual by Mitchell & Wightman (UK) and On Book Design by Richard Hendel.

During the 20th century some of the larger type foundries, typesetters, and printing companies produced typographic style guides, which occasionally addressed the layout of book pages.

For instance, the 1923 Linotype Manual of Typography shows various types in actual size page layouts.
So too does Book Types from Clowes (a British printer), 1935.
And The Western Type Book (Western Printing Services, Bristol, UK [West England]), 1960.

All these were hard-bound type specimen books of 200+ pages.

That practice is gone, for economic reasons related to technological change.

Today, the standard is represented by Robert Bringhurst's The Elements of Typographic Style.

Positioning his work in a similar manner to that of the style guides for editors (e.g. Strunk and White), Bringhurst covers many aspects of typography, including the page layout of books.

I suspect the quote should be "the suitability of type design to the subject of a book is no less important than the nature of its text"; and it is true that, for example, the use of William Morris' Golden type - or something very similar, such as Jenson Oldstyle - in a book on higher mathematics would be as jarring as an excessively informal writing style.

Hobo, Papyrus, President or even Freehand as a text face would, of course, be even worse. And yet, the American Mathematical Society, in commissioning a typeface for the printing of mathematics, ended up with the unconventional AMS Euler, with a calligraphic effect.

However, egregious errors in the former are even less common than egregious errors in the latter. A typeface such as Palatino, for example, would seem to do well in either a textbook or a novel.

Get a copy of Robert Bringhurst's "The Elements of Typographic Style" and Jost Hochuli's "Designing Books": both essential readings for anyone willing to design books.

Another essential book I forgot to mention: "The Form of the Book" by Jan Tschichold. The English subtitle - "Essays on the Morality of Good Design" - says it all.