it's important to realize that you're not doing anything wrong. some dogs are reactive as hell and usually it's because they are poorly socialized, which leads to really annoying behavior habits like loudly challenging everyone and everything in their sight line. for reference, i am the guy that gets along with lots of dogs/animals, including the ones that have reactivity, socialization and trauma problems. like dogs that are aggressive to men never seem to put me in the man category. even so, there are individual animals and contexts that are no-win and the best you can hope for is a situation where neither party feels antagonized.

if you have a good relationship with your neighbor, you can try to work out some formal socialization times where you learn how to interact with each other and pick up some nonverbal, low effort tactics for getting the dog to shut it's cram hole. if you're not friendly with your neighbor, your options are much more limited. the fence is a very real physical and cognitive boundary.

as others have said, being or at least imitating calmness and an assertive countenance is key. animals aren't psychic. they are master interpreters of nonverbal cues, though. also, generally, giving attention is a "reward" for good behavior, so ignoring them (in terms of body language) when they are being crappy can be helpful.

some people have said using a higher pitched tone is interpreted as "friendly", but i don't agree with that being universal. talking friendly to a dog you don't know can work, but it might also confuse them or wind them up. calm voice. calm tones. as best you can. if you can't, just orient yourself and go about your business as if you don't acknowledge their existence or care what they're blabbing about when they're being annoying. also, don't do a lot of eye contact. if you want to keep an eye on them, look near them all you want with your head off axis and let your eyes do the work, maybe a quick glance, but don't lock eyes like a cult leader or an MLM recruiter.

and, above all, garden whenever you want. wear ear plugs if you want. that's your back yard. if nothing else, time and repeated exposure can make them less reactive to you puttering around. patience is key. their concept of time is a mess. play the long game with that big brain of yours.