The Spanish equivalent of It seems that they hate each other is Parece que se odian.
In both languages seem/parecer are one-place predicates (well, both can optionally accept a second argument with the role of an Experiencer, as in It seems to me that they hate each other/Me parece que se odian, but this is irrelevant to the present question and can be ignored here).
Thus, again, in both languages, under the monadic reading of seem/parecer, the only real argument is discharged by the clause introduced by that and que, respectively, which appears post-verbally and, in English at least, clearly occupies the 'complement of V' position. Whether that is also the case in Spanish is less obvious, and will be the focus of this question, but allow me first to briefly complete the scenario in which doubt may arise in this respect.
In both languages, therefore, the subject position is non-thematic (no argument = no theta role), but a difference arises at this point: English being a non-pro-drop language (= the Extended Projection Principle of Chomsky's early GB/P&P Theory), in English the subject slot must be occupied by a pronounceable 'dummy' (it, in this case), whereas, Spanish being a pro-drop language, no 'dummy' is required - nor possible, under Economy - (cf. *Ello parece que se odian) and so Spanish clauses of this type apparently have nothing in subject position.
Also, in both languages, raising the post-verbal that/que clause into subject position cf. That they hate each other seems and Que se odian parece, respectively, leads to ungrammaticality. The reason, however, has nothing to do with the raising of the clause itself, which is allowed when the predicate is 'heavier', as in That they hate each other seems evident/Que se odian parece evidente; what blocks the promotion of the clause to subject position in such circumstances is the 'lightness' of the predicates seem and parecer, i.e., that constraint is a matter of not leaving an informationally 'light predicate' like seems or parece in the VP Focus (= default end-focus) position, which, by definition, must add informationally 'substantial' content.
Having said this, I think, my readers will be ready for the issue that interests me and the question(s) that I want to raise.
The fact is that whereas, in English, as stated, the clause undoubtedly sits in the complement of V position, in Spanish, where focused subjects are regularly post-verbal (cf. Ha telefoneado tu marido = lit. Has phoned your husband) the que-clause might arguably be either a complement or a post-poned subject, and, therefore, evidence is needed to determine which of those hypotheses is right.
Now, in English, a standard test for the complements/attributes of verbs like seem is that they can be replaced by so. Hence, in a dialogue between A and B, A might remark It seems that they hate each other and B might, in case s/he agreed, say (Yes,) So it seems, or, in case B did not agree, s/he might reply It seems so, and perhaps add but [I know that] they do not [really hate each other]. In any case, however, what is left in situ/raised into the Focus position at the front of the clause is not the subject, which remains it in both cases, but the pro-form so standing for the that clause in complement of V position.
In the case of Spanish, the standard pro-form for definite direct objects of transitive verbs is one of the paradigm le/la/lo, and, clauses being neuter gender, it would be lo, and the standard pro-form for attributes of stative verbs like ser or parecer (this case) is also lo. Spanish, unlike English, completely neutralises the D.O./Attribute opposition (in this respect).
Hence, if we wanted to translate the English dialogue between A and B above into Spanish, one of the possibilities would contain the exchanges A: Parece que se odian. B: Sí, lo parece, and, in that case, the Spanish que-clause would reasonably be analysable as the complement/attribute of parece. However, that rendition of the English A<>B dialogue is not the only possibility; B might also reply Eso parece, where eso could just as easily be understood as a pro-form for an (in this case post-poned) subject, rather than an in-situ complement/attribute of parece.
Furthermore, at least according to my (and my wife's) native speaker intuitions, that choice is not a free one: the 'unmarked' choice is eso, and lo is only an additional 'marked' option. In other words, Lo parece would be the Spanish equivalent of English It seems so (but...), and compatible with B's addition of something like pero yo sé que, en realidad, no se odian (= ..., but I know that they don´t really hate each other), whereas Eso parece would be the Spanish equivalent of So it seems, and (in my and my wife's Spanish), incompatible (or not easily compatible) with any addition of B's like , pero yo sé que no [se odian/es así].
This leads me to the conclusion that, in the unmarked case, the Spanish que-clause that follows parece is actually a post-poned subject, not a complement of V in situ, although there is a marked construction that allows it to stay put in the complement of V slot (and, in that case, be replaceable by the pro-form lo characteristic of all Spanish neuter and definite direct objects and attributes).
Unfortunately, under the traditional view that such that/que clauses are initially generated as complements of seem/parecer, that analysis leads to a serious theoretical problem, because the would-be unmarked construction (i.e., that in which the que clause is raised from its complement of V position and postponed, with or without an intermediate 'stay' at the pre-verbal subject position) actually requires more computation than the would-be marked one (i.e., that in which the que-clause stays put after parece and no further computation is needed).
This unexpected result puzzles me, and I would like to know, first a) whether other native speakers of English and Spanish share the intuitions described above (because, if no other native speakers do, the theoretical problem changes, it becomes 'How can my Economy-driven Language Faculty have allowed me to develop such an uneconomical construction?'), and then b) whether there is any way to avoid my conclusion that Spanish que-clauses following parece (but not parallel English that-clauses following seem!) are postponed subjects in the unmarked case and complements only in the marked one, and thereby to remove the Economy problem just described.