There are a few ways to interpret the original post question:
If you short 2 probes of your voltmeter you will get 0 V difference, correct? If you now place your 2 probes in the ground, depending on what you are touching (rock, sand, soil, etc.) on each end of the your probe, and how far apart your probes are.... I am sure they will no longer be showing 0 volts. Now space them 1, 2, 5 meters apart.... 10 meters.... 1 kilometer. Will it still show 0 volts? So is the Earth electrically neutral... well, compared to what? Compared even to Earth at different places it is not. It may be close... but unlikely to be 0.0000000000 V.
Taken to the extreme, if you stuck one probe in China and the other in the USA and could measure the potential difference (never mind all the other problems with this analogy... just bear with me a second).... again I am sure they would not show 0 volts difference.
Why? There must be influence from electron distributions through different soil, rocks, effect of atmospheric discharges and polarization/capacitive charges due to cloud cover, and convective currents through the mantle and interior to the Earth's crust due to flow of magma. Essentially, the Earth itself has some unequal distribution of charges within it due to various influences and it takes time for them to flow and neutralize to balance out. Sometimes it may actually not be able to easily flow due to properties of different minerals and dielectric materials in the ground from region to region. And even if it did, the effect of atmospheric static electricity causing charge movement within the crust will also affect what you consider "neutral" compared to another part of Earth some distance away.
So another way to interpret the question is if you ADD ALL POSITIVE AND NEGATIVE CHARGES of the entire planet including the atmosphere and the surrounding ionosphere up to a distance of 50 km into space, do they all balance out? Unlikely. Again you constantly have a solar wind hitting the magnetosphere, with particles deflecting all over the place. Who knows what the overall balance of charge really is, and whether it gets skewed one way or another.
How about the entire solar system then? Add up all particles in the entire solar system out to furthest reaches of barren inter-solar-system space... Does the total balance out? Same number of electrons as protons? And what about other charged particles? Good question. You would think conservation of charge would need to be observed so if it started equal, it would have to remain equal (barring any influence from external particles coming in with charge). But we don't know.
For all we know there may be a net imbalance but we'd never notice unless somehow on Earth we had it as well and could take extremely careful measurements and see that indeed.... there are more electrons than protons, but for whatever reason they seem to be sticking around (like a huge static charge on the Earth) because there is not enough of an imbalance to cause a sufficient mutual repelling of charges to drive them out of the region of Earth.