I heard a rumor that some people use this to check their neighbour's revenue and sometimes make snark comments if one of them has a high revenue but lives in a "average revenue" part of town.

They'd say that if you earn a lot, you shouldn't take a cheap housing.

Any truth to that?

There used to be a lot more of that, but a system was put in place where you have to identify yourself with electronic ID to access the information, and the information is logged so the other party can see it.

Nowadays I think mostly journalists use it to pull up information about politicians and other people that are in the public spotlight. There are of course the yearly "richest people in Norway" lists in various categories.

Making snark comments about that sounds very unlikely. More likely they'd have respect for someone living frugally and not showing off. See https://en.wikipedia.org/wiki/Law_of_Jante

Yes and no. You get notified if someone else actually asks for your revenue info and so in practice nobody actually does it.

What is the harm in this case? Shit people are shit even without information. They would be snark about something else then.

Yep, that tracks.

There's also the underlying current of Jantelagen (Law of Jante) https://en.wikipedia.org/wiki/Law_of_Jante