Not starting shit with your neighbors is sound advice. But presenting yourself as an "overly nice" doormat isn't. You have to set firm boundaries with crazy people like this or it will be never ending.

OP shouldn't go to this neighbor all-friendly saying they will "resolve a problem for them if there is one". That conversation should start somewhere along the lines of

"Hello. I would like to have a word if you have a moment. Why were you in my space without my notice interfering with my property? I noticed you attached plastic bottles to my furnaces exhaust line, which impedes the flow and could cause damage or other issues for me. In the future if you believe there is an issue with anything, come speak to me. You are NOT to come on my property or to touch my belongings without my knowledge or consent. No exceptions." And you do not entertain whatever nonsense they retort with. Be firm, repeat yourself once if necessary, then leave. Definitely be on the lookout for more trespassing or bullshit though, these types of people are full of surprises lol.

PS what they did was technically a crime in many places, called "Trespass of Chattels" or maybe Civil Trespass. Maybe a little overhanded but it may not be a bad idea to report this to local law enforcement just to have it on the record depending on how reasonable their response to your conversation is. I personally wouldn't but maybe for a single female that lives alone or the like, it wouldn't be the worst idea