Don't tell your dog off, you're just increasing the stress levels in an already stressful situation and/or he thinks you're joining in. You can't ignore it either because responding is self-reinforcing, and he will start to go out there looking for stuff to bark at.
Go the other way - make hearing next doors dog the BEST thing that can happen out there, pair it with high value treats and fun from you. This is classical counter conditioning, pairing the currently upsetting event with something really really good until your dog thinks this other dog barking/growling/making noise is a great thing and he actively feels good about it.
Don't wait and see if yours barks, then take action.
Don't ask yours to shush then reward.
Literally, pair next door noise with treats, until your dogs automatic and instinctive response is to look to you and he's feeling good, and when that happens the barking will stop anyway.
Then you start to fade out the free treats for hearing this dog somewhat, so its the loudest/weirdest/most aggressive sounds that get treats, and the say 5% quiet noises, they get either nothing or you asking your dog to sit/watch me/lie down to earn the treat.
Gradually you shift that ratio of free treats to earned treats/no treats over, going from easiest, least up setting to loudest. I would probably seek to maintain rewarding very loud volleys of barking, rattling bins, thunder, most of the time, for life, with all dogs, so we keep that association.
For now this does mean that if he's out there, you're out there and you have a full treat pouch on you. If you need extra security to end the situation swiftly, use a long line clipped to your dogs harness so you can bring him in if he is too far into barky territory to perceive the rewards as rewards.
No shouting, no cues to do anything, absolute consistency.
YOu should find that after a week or two, his responses to next doors dog are massively improved and after a month or so you can drop the extreme levels of consistency.