Lets tale a step back.
A spin-0 particle cannot have a dipole moment, either electric or magnetic, because there is no direction in which it can point. A similar argument can be made (more mathy) to show a spin-1/2 particle can have a monopole monent (charge), a dipole moment (electric or magnetic) but no higher moments. EDMs open a can of worms that is a big distraction - if you want to discuss them, that should be another thread. So we have MDMs.
The neutrino MDM is measured to be close to zero. As close as we can get. Since magnetic moments go as 1/m, and neutrinos are light, if there were any new physics effect, it should be large. Since we see no evidence whatsoever for this, we know it is very, very small. I do not know what the most stringent limit is, but if the neutrino had even a tiny MDM, the process ##\gamma \rightarrow \nu + \overline{\nu}## would go on all the time. Since we don't see it at all, it either does not happen, or happens way too rarely for us to see it.
In either case, the process is far, far too weak to be seen in a S-G experiment. If this were not the case, we would have seen it elsewhere.
Note that this is the same question as "How do we know that neutrinos are neutral and not almost neutral?" Same answer - "almost" is so close to reality that in virtually every case it does not metter.