First a correction. In my previous post here I made (at least one putatively) false statement. I said that "the scientific evidence we have supports SR". According to Monton ("Presentism and Quantum Gravity" in The Ontology of Spacetime):
The special theory is a decisively refuted theory of the nature of time. Special relativity is incompatible with such phenomena as the gravitational redshift and gravitational lensing, phenomena that provide evidence for general relativity.
If this claim is correct, then whether or not presentism is incompatible with special relativity is simply irrelevant to the question of whether presentism is true.
Sider (4-Dism, p. 42) runs afoul of Monton's claim when he takes SR to deal a deathblow to presentism:
I turn finally to what is often (justifably, I think) considered to be the fatal blow to presentism: that it is inconsistent with special relativity... Some presentists have said: so much the worse for special relativity, at least in its Minkowskian formulation. Perhaps future empirical research will bear out this position, but in cases of science versus metaphysics, historically the smart money has been on science. At any rate, the present discussion will assume that consistency with something fairly close to current physics is a constraint that must be met by any adequate theory of time.
Of course, I've never been convinced that current formulations of SR are incompatible with presentism, although I'm open to the idea. I'll need to think more about that. But let's suppose that SR is, as currently formulated, trivially incompatible with presentism. It should be observed that both SR and GR can be modified by adding structure to the spacetime models. For adding additional structure will yield a theory that is empirically equivalent with the current formulations of GR and SR. So it will yield a theory that is "fairly close to current physics".
Such a change will do away with any trivial incompatibility with presentism. And though it would be scientifically revisionary, it wouldn't be revisionary in any interesting philosophical sense, for there is no scientific evidence (given the empirical equivalence of the current theory with a the current theory plus some additional structure) that tells against making such a revision. (At best, there may be a lame appeal to simplicity available.)
Sider discusses five ways the presentist might try to revise SR to render it compatible with presentism. Only one of the options he considers has ever been entertained by any serious presentist, as far as I know. Thus four of the presentist/Minkowsian hybrids he discusses are just not relevant to the compatibility of presentism with SR. Of interest is his "Hybrid 2". The presentist who endorses this hybrid claims that only one spacelike hypersurface (into which spacetime is foliated) exists.
Now Sider's main objection to this hybrid is that it is "scientifically revisionary" since it introduces a relation of (distant) absolute simultaneity. For on this view, we can say that event x and event y are simultaneous iff x and y coexist. Now this is interesting, for several reasons. First, I take that revising SR and GR in the fashion we have (see fn. ) doesn't yet introduce a relation of absolute simultaneity. For that, one needs to privilege a particular hypersurface, as the presentist wants to do. Is there any scientific evidence that rules out privileging a particular hypersurface? I know of none, though I'm open to hearing about it. If I'm right that there is none, then Sider's claim isn't of much philosophical interest. For we have again have a case of something being "scientifically revisionary" in the sense in which we've converted a scientifically accepted theory T into a new theory T* which is itself empirically equivalent with T and includes T. It is at least fair to say that, in such cases, the scientific evidence we have which supports T can't settle the question of whether T or T* is true. And so scientific evidence provides no reason to reject T*. (These last two claims are intentionally carefully formulated for philosophical reasons.)
Let's now return to a point made in the last entry: Sider's criticisms of presentism frequently smack of a commitment to some degree of verificationism. Why should we think that there is no relation of absolute simultaneity, given that there is no scientific evidence for disbelieving this? When Einstein dispensed with this relation, he did so on decidedly and obviously verificationist grounds. According to Einstein, we should not admit a relation of distant absolute simultaneity if it is empirically impossible for us to verify whether distant events are simultaneous. Thus he proposed his revisionary "radar test" definition of simultaneity: roughly, event x and distant event y are simultaneous iff light pulses sent out from each event would strike an observer situated at the midpoint of the line connecting x and y at the same time.
Now this is obviously not what it means (in ordinary language) for events to be simultaneous. It's, at best, a method for determining whether events are simultaneous. As a definition of "simultaneity" it's just obviously ridiculous. Einstein has proposed a poor revisionary definition of "simultaneity" for purely verificationist reasons. He thinks that it would be meaningless to say that events are simultaneous if we couldn't (in principle) empirically determine whether or not they were. But I see no reason to endorse this verificationism (and it's a philosophical claim, not a scientific one). And if I do wish to speak of "simultaneity" in this sense (perhaps so that I can converse with physicists), it would be foolish of me think it had any bearing on the sense of "absolute simultaneity" which presentists care about. So it's not even clear that there is real disagreement between scientists and presentists on this point.
The presentist can claim that two events are absolutely simultaneous iff they both exist. They can claim that two past events (which don't presently exist and so don't exist simpliciter) were simultaneous iff they occupied the same hyperplane. And similarly for future events. (The presentist has a standard solution to ontological commitment for such claims. They are not ontologically committed to the existence of objects that occur within the scope of past and future tense operators.) To reject this kind of appeal to absolute simultaneity as scientifically revisionary strikes me as (i) misguided, (ii) unbacked by any scientific evidence, and (iii) question-begging.
Finally, it's not at all clear to me that Einstein's revisionary definition of "absolute simultaneity" does let us determine, even in principle, whether events are simultaneous (if GR is true and space is non-Euclidean). For to make such a determination, we would need to know what the structure of spacetime is between the two events in order to find the midpoint of the line connecting them. And on his theory, this would require something like a known solution to the n-body problem for any (possibly infinite) n, or else omniscience. So I doubt whether it meets the verificationist demands he wished to impose. Even his definition may well not be empirically meaningful (not that I take that as mark against a definition, since I don't worship at the altar of Ayer). I think this is right, but I wouldn't endorse the claim in official print. Comments are very welcome here.
Thus far, Sider's case against presentism isn't winning me over.
 The additional structure needed consists in partitioning the current models of Minkowskian spacetime into hyperplanes of simultaneity (i.e., foliating spacetime into an ordered set of spacelike hypersurfaces).