Would climbing onto fighters placed on display cause damage? The question is about any more or less modern plane similar to Su-27 in its fuselage design. It's not uncommon to install retired planes as monuments. Here's one example in Eastern Europe (image from this post on some local Reddit equivalent):



The shot shows a retired Su-27 which had its engines and electronics removed and was installed on a pedestal somewhere in a city. It's not uncommon for locals to climb both such pedestals and the planes - youngsters do this for lulz and also to make photos of themselves. Standing and sitting on wings or behind the canopy are typical examples.

I guess this is not very good for the airplane fuselage. Not only will paint get damaged but also the fuselage may be mechanically damaged - mostly metal sheets might be bent.

I know that it's possible to accidentally fall from a plane, especially when it's wet because or rain or melting snow, but let's ignore that in this question. I'm only asking about what's good or bad for the plane.

How bad for such a plane is climbing it by an unprepared person (who doesn't know where exactly it's safe to step)?
If you intended to make the aircraft airworthy again, yes, it can cause major damage. But, for use as a static art display, it would be no different than any other display really. Most likely all the moving parts have been fixed so they don't move so making it airworthy again is pretty much impossible.