[1] This was also the philosophy promoted by X in his famous book Small is
Beautiful, [published in the 1970s].
[2] This was also the philosophy promoted by X in his famous book Small is
Beautiful, [which was published in the 1970s].
The simple answer is no. Generally, "that" can be omitted in defining relative clauses providing it is not functioning as subject of the relative clause. But that's certainly not the case with non-defining relatives, which do not permit "that" but only wh relative words which cannot be omitted. In any case, your first example does not actually contain a relative clause.
Although your examples have similar meanings, and their subordinate clauses both refer to X's famous book, only [2] contains a genuine relative clause: in [1] "published in the 1970's" is not a relative clause that has its relative word and finite verb omitted, but a different type of clause altogether called a past-participial clause.
Note that the past-participial clause is a bare passive, as evident from the admissibility of a by phrase.