It's common sense that there is absolute simultaneity, whether directly so or because it's common sense that there is an objective present. It is sensible for philosophers to want to hold on to what is common sense. But here we should not be so quick. For consider some common sense claims:
- There is absolute simultaneity.
- If A and B are absolutely simultaneous and C and D happen t units of time after A and B respectively, then C and D are absolutely simultaneous.
- Properly functioning clocks correctly measure lengths of time.
- Clocks continue to properly function when moving, as long as they are not accelerated so quickly as to damage them.
Now when a number of common sense claims cannot all be held together, it is not responsible simply to say that one of them is common sense and therefore true. For the same thing could be said about the others. One would need to say something about how one's preferred claim is more commonsensical than the others, and that's a judgment that may well go beyond common sense.
I think most defenders of absolute simultaneity will reject (3) or (4). But if we look at how we actually acquire our concepts of durations of time by using clocks, watches and internal timers, it's plausible that we are committed to (3). And our practices of blithely using clocks even after coming to think that the earth is rapidly moving around the sun suggest (4).
I actually think that an interesting strategy for defending absolute simultaneity is to deny (2). This would lead to a view with absolute simultaneity but purely relative temporal durations.
That said, I am happy to deny (1).