Easements can be deeded easements, which means they are subject to conveyance, and have intrinsic value, or they can be easements by necessity. It is unclear if the easement was created by a simple use agreement, or if it is one of necessity. For the most part, the simplest rule to follow about long standing easements is don't block the easement, build fences or place gates across them, and you won't have trouble. If worse comes to worse, you can always seek judicial intervention to define the rights and responsibilities of the parties vis-a-vis the easement, but it seems that acting "neighborly" as you put it, might be the easiest way to go.
In Washington, the parameters of an easement are determined by the intent of the parties as expressed in the recorded easement document. The dimensions, precise location, and purpose of the easement should therefore be be determinable from the description in the easement agreement itself. Your warranty deed's legal description likely only references the easement as a "subject to" restriction, so you will likely need to obtain a copy of the recorded easement document in order to figure out what your options may be. For instance, if the easement is for ingress/egress only, and doesn't include parking, your neighbor's objection may be well founded. You should consider obtaining the easement document and discussing your options with an attorney, including the possibility of negotiating a use and maintenance agreement with your neighbor that would provide a framework of rules for use and upkeep of the driveway area that would be mutually acceptable to you and your neighbor.