To derive Einstein causality, as used in the proof of Bell's inequality, one can apply some relativistic symmetry principle to the notion of causality. There are different variants of relativistic symmetry principles, which we want to consider here, to find out which variant should be used.
We distinguish here three variants of the relativistic symmetry principles:
The specification of the meaning of "having relativistic symmetry" is not important for the points we have to discuss here.
Let's consider now the question which of these relativistic symmetry principles are important for our discussion.
Most formulations of relativity principles in the literature are variants of the first, weak relativity principle. This includes even the "strong equivalence principle": The meaning of "strong" in this context (inclusion of gravitational experiments) is simply different from the meaning of "strong" used here.
For the discussion of realism, weak relativistic symmetry is not important at all, simply because there is no contradiction between them:
Weak relativistic symmetry is not sufficient to prove Bell's inequality. Therefore, there is no contradiction between weak relativistic symmetries and realism.
On the other hand, weak relativistic symmetry is the only one which can be explicitly tested. Of course, every test of weak relativistic symmetry also tests the stronger principles, a falsification would falsify them all. But the difference between weak relativistic symmetry and the stronger symmetry principles cannot be tested.
Realistic relativistic symmetry already allows, applied to causality, to derive strong Einstein causality. Therefore, it is in conflict with realism.
But, if we reject realism, what remains from realistic relativistic symmetry is only weak relativistic symmetry. Indeed, what remains as important, if we have no hidden real objects, are only observable objects.
This allows a decisive argument against the rejection of realism, following the principle of minimization of losses: We do not loose anything if we preserve realism, and replace strong relativistic symmetry by weak relativistic symmetry, in comparison with the alternative. The rejection realism leads, as a consequence, to the same replacement of realistic relativistic symmetry by weak relativistic symmetry. Or, in other words, we have to replace realistic relativistic symmetry by weak relativistic symmetry anyway, and, after this, we have no reason at all to reject realism as well. Moreover, giving up realism, we would also loose, as well, realistic classical causality.
We do not need to evaluate how much we loose giving up realism, simply because giving it up gives no gain at all.
Thus, after the removal of strong and weak Einstein causality, together with strong and weak relativistic symmetry, the only principle which remains relevant for the discussion (as a principle in conflict with realism) is manifest relativistic symmetry. Only for manifest relativistic symmetry there remains, after a rejection of realism, a nontrivial difference to weak relativistic symmetry. Therefore, the argument against strong relativistic symmetry no longer works: If we reject realism, instead of giving up manifest relativistic symmetry, we gain something else — the non-trivial difference remains between weak relativistic symmetry, which is only about observables, and manifest relativistic symmetry, which is about everything used in the theory.
Therefore, to decide between manifest relativistic symmetry and realism, we have to compare two different losses, each of them at least non-trivial.
But if one does not consider manifest relativistic symmetry (different from weak or strong relativistic symmetry principles) as an important principle, the decision should be obvious: One has to preserve classical realism and to give up the principle of manifest relativistic symmetry.