When people mention the neighbors, you say the guineas/turkeys won't be going into the neighbors' yards but into the woods. But when people mention the woods (the local ecosystem), now you say it's not the woods but the neighborhood... So where will they be going then? If they're in people's yards, it's a problem of intrusion and bird shit on their property. And if they go into the woods, then yes the woods absolutely are a local ecosystem, where domestic birds don't belong. It's a problem either way. They belong on your property.
Sharing the same niche as wildlife actually argues against your point, not for it. If they are in the same niche, then they are in direct competition with wildlife. Domestic birds/animals are usually larger and bolder than their wild counterparts, and push them out of an area. Animals are territorial. If a pushier animal comes into an area, it forces the local animals to leave, depriving them of the resources of that area and putting them in conflict with other animals whose territory they've now been pushed into. It's not just about the people-centric costs and benefits, like ticks. Nature is a balance act that includes a lot more than us.
The settlers aren't exactly role models to be followed. They brought all kinds of pest species with them and let them loose, they destroyed the Northeast's forests to clear land for agriculture, and caused untold damages to all kinds of American ecosystems. We should be looking to the past to learn from its mistakes, not to justify making them all over again.