Would it make sense for me to tell my new neighbors to respect my property?
What have they done that is disrespectful?
They use my lawn furniture without permission.
Someone using my stuff without permission would annoy me too. It's really rude of them. It's fine to talk to them about it.
They told me that I'm the criminal one, but they're the ones using my things like it belongs to them!
You are definitely in the right to ask them to respect your property and stop using your lawn furniture. Just do it in a respectful manner so you don't start a neighborhood feud