I haven’t really dug into this much, but you can formulate SR as if an ether exists: Lorentz Ether Theory (LET). Since the mathematics is the same, there is no experimental way to distinguish between LET and the conventional interpretation of SR. However, as far as I know no one has formulated a version of GR and QFT that is consistent with LET, though it’s not clear to me whether that’s because of a fundamental incompatibility or just because not enough people have tried. We have discussed this topic in the past: Science and the Metaphysics of Time. @PdotdQ might be able to say more, since he’s actually a theorist.
Secondly, there might be philosophical arguments for having a preferred frame of reference. LET in particular has been championed by William Lane Craig because he prefers an A-theory of time (where there is an absolute “now”, instead of past, present, and future being equally “real”). That being said, LET is not the only way to argue for A-theory, for example Edward Feser in his book Aristotle’s Revenge for example lists up to four possible ways to philosophically interpret SR such that one still retains a preferred reference frame.
Needless to say, the majority of physicists don’t care much about philosophical arguments for preferring LET over conventional SR, because physicists usually only care about the observables, and SR is more practical and elegant compared to LET.