When visiting a neighbor, I think one should bring essentially an equivalent to what they might consume. for example, we brought a bottle of wine with us to our neighbors boat, but had a couple of their beers. They never opened it, but we left it for them.
I would never expect a guest to bring their own tableware, unless I asked. I would if we were short, otherwise, washing dishes is a simple price of being social.
Here is my biggest advice and pet peeve. Never ever ask or expect to take back the remainder of whatever you brought that wasn't finished. There may be an exception for something very valuable that wouldn't be expected to finish, such as bringing your half consumed bottle of Remi XO for after dinner drinks. However, your contribution should be approximate to accommodate your overall consumption and planned to leave behind no matter what.
For example, we had a couple bring a pie. We served about half of it to the four of us and when leaving they quickly grabbed what was left and took it back. We, however, served coffee and after dinner drinks to them and were taken back by them rescinding about $2 in pie. Yes, we also washed the dishes they used.