What the book says is an interpretation consistent with the teachings of the EBTs as found in MN 117 & SN 12.17, which was already provided for your study. The book says:
He spoke in the language of relative truth in order to teach morals to people still befuddled with the idea of eternalism – those who feel that they are selves, that they possess things. Such people feel this way to the point that they habitually cling to these ideas and become attached to them.
MN 117 says:
And what is right view that is accompanied by defilements, has the attributes of good deeds, and ripens in attachment [acquisitions]? ‘There is meaning in giving, sacrifice, and offerings. There are fruits and results of good and bad deeds. There is an afterlife. There are duties to mother and father. There are beings reborn spontaneously. And there are ascetics and brahmins who are well attained and practiced, and who describe the afterlife after realizing it with their own insight.’
I already posted a relevant meaning of “eternalism” found in SN 12.17:
Suppose that the person who does the deed experiences the result. Then for one who has existed since the beginning, suffering is made by oneself. This statement leans toward eternalism. (Sujato)
Kassapa, if one thinks, ‘The one who acts is the same as the one who experiences the result,’ then one asserts with reference to one existing from the beginning: ‘Suffering is created by oneself.’ When one asserts thus, this amounts to eternalism. (Bodhi)
SN 12.17
Buddhadasa obviously knew MN 117 because I happened to visit his monastery in 1989, when Buddhadasa specifically used MN 117 for his Asalha Puja Day lecture. Here, Buddhadasa repeatedly referred to the Noble Right Concentration With Seven Supporting Factors and whose primary purpose was to explain, from MN 117, that “Right View Comes First”; emphasizing the focus should be on panna-sila-samadhi-nana-vimutti rather than on the Theravada standard of sila-samadhi-panna . Personally, I first learned Buddhadasa was speaking from MN 117 in 1993, when I first read the PTS Majjhima Nikaya in Bangkok.
Its perfectly OK to critique Buddhadasa but I suggest to avoid the attitude of: Because something he said may be wrong means everything he said is wrong.
I recall Sujato has posted on this forum there was a time Buddhadasa was one of the only monks in Thailand studying & following the Suttas. Therefore, if a person is not fluent in the Suttas, it’s probably not wise to not attack Buddhadasa on his sutta interpretations. Probably 90% of the time the attacker will be wrong and the other 10% of the time merely guessing.
Santikaro is certainly not the only person to ‘confront’ Buddhadasa on the issue. I happened to be in the audience when another Western monk asked Buddhadasa about rebirth. Buddhadasa maintained silence a few times then, when pressed again, said the doctrine of rebirth is useful for morality.
The point I made about Santikaro is the Suttas already answer what occurs after “death” (“marana”). Therefore, for Santikaro to ask Buddhadasa such a question shows Santikaro was probably not fluent in the Suttas. Keep in mind Buddhadasa passed away in 1993 and Santikaro obtained Bhikkhu Bodhi’s first edition of the Majjhima Nikaya in 1995. Santikaro was a translator, teaching monk & social activist whose primary reading of Sutta when Buddhadasa was alive seemed to be only those suttas he translated from Thai to English for certain ‘From His Own Lips’ articles in his ‘Evolution Liberation’ series; or otherwise quoted in live Buddhadasa public talks (such as the January 1989 talks on the Four Noble Truths) . Examples are here: