I say again, wide binaries are a terrible test.
Let's go back to the basics. In the Newtonian word, I have two masses, M and m, separated by a distance r, and for simplicity, let's have them at rest. The heavier feels an acceleration Gm/r and the lighter GM/r and two lines of algebra should convince you momentum is conserved: no external force, and the center of mass doesn't move.
In MOND, the accelerations are GM/r and something else (assuming the acceleration is in the deep MOND domain). I think it is \sqrt{GMa_0/r} but it doesn't matter exactly what it is. The point is now that the center of mass starts to move, with no external force.
Nobody believes this is what happens. Nobody.
I think even the MOND proponents would argue that something must happen to prevent this, and that the equations we use for MOND are probably approximations for real, better-behaved ones.
This is part of the reason I say that MOND has problems with composite objects. (We can discuss why rotation curves are particularly ill-suited to sort this out).
So looking at wide binaries is exactly where we know that MOND prediction needs to be altered. It's just a bad test.