
As long as you keep doing what your doing, not letting him bark for prolonged periods or at unsocial hours (11pm to 7am) then your dog is allowed to bark.
With mine (6 medium size spitz) they too can be reactive to other dogs barking, especially the two year old youngster, and the local cats enjoy winding them up too.
My rule is if they bark they are brought straight back indoors. It's the only way. I too have a neighbour next door but one who can be heard shouting at the dogs (mine, my next door neighbours Russels, the dobe on the end, and any one else's).