The frequencies your neighbor would be transmitting are different than the ones your own communications would use. They should not interfere with your utilities.
Occasionally, funny things like old metal connections can end up re-broadcasting related frequencies instead of the original one, but this is usually accounted for as well when the allocations are made between TV/amateur/cellular/etc. bands.
It is encouraging that the neighbor not only appears to be a "ham" (trained and licensed hobby radio operator) but is also a professional RF engineer, so I doubly doubt you should have any problem. A big antenna like that would used for frequencies no where near the frequency of your WiFi. And it would be extremely unlikely for a wireless radio signal to interfere with an optical fiber internet connection itself.