I don't agree with them, but increased density is absolutely a "threat" to the character of any neighborhood, not just something they "view" as such. Having more people live in a neighborhood changes everything about it, I don't understand why people neglect this point, like it isn't real or maybe doesn't count because everything NIMBYs say is invalid because we all want cheaper rent. But I am not saying you're doing this, it's just what I see when people talk about NIMBY.
As a result of denser housing, rent should go down N%, but your quality of life (if you're not fooling yourself) will also go down slightly as you have to deal with the reality of living near more people. (Longer waits at local stores, more crowded sidewalks, etc. We can pretend this is a "good" thing and that humans are social creatures, but there is a point where it becomes less tolerable to most people.)