When my neighbor turns his sprinkler system on it vibrates the pipes in my house.

Have you checked to be sure they are not tied into your water system.

They should not vibrate. As Chuck tells you in his post, they are probably tied together - and they should not. If they do, he is stealing your water. Each house should have its own plumbing system. Investigate. Find connection to your system and cut it off. Back to you . Milo