I still think old shitty statues and stuff should be put in a museum or something

I don't think anyone has a problem with that. But, that's usually not what the regressive types are complaining about.

To use the US example, the overwhelming number of "Confederate Monuments" were erected many decades after the Civil War, and typically funded by white supremacist groups or their close allies in city and state government. They were installed in public parks, on public easements, in front of public buildings, etc. Notably, they are typically not on graves, old battlefields, etc.

Folks quite reasonably think we should remove monuments that were put up as a big "F U" to remind black folks who is really in charge. These statues are certainly shitty, but they also are not "old". They're much younger than the people/conflicts they memorialize, and have no historical significance (except to the white supremacists who put them there).

Of course it's not just the US. I remember in the wake of the collapse of the Iron Curtain, communist sympathizers complained at the removal of Soviet monuments. I remember college professors complaining at the renaming of Leningrad back to St. Petersburg, calling it a "dangerous right-wing move" and an erasure of Lenin's history and legacy.