It matters how statues come down as much as it does what the statues represent. If a statue is removed after lengthy community deliberation in formal proceeding, that is different than a crowd on the street yanking it down. It also matters that some have been debated a long time.
But the context is important in each case. Some statues - Confederate ones especially - were given extra protection by state governments even though local communities voted repeatedly to remove them. Crowds removing them can be said to represent real community sentiment then.
But when a crowd just randomly chooses statues to tear more troubling. It's not surprising that the most idiotic statue destructions - Hans Heg or Grant - were done by vandals with no community deliberation. Another point to consider is the entirety of the statue and its context.
The media has described the statue at the Museum of Natural History as the "Theodore Roosevelt statue." That's simply incorrect. It's not a TR statue. It's a statue of TR and two other men designed to look like barbarians next to him. There's a reason it was debated for years.
Same with the emancipation statues in DC and Boston. In those cases there are genuine differences in the African American community, not over whether "an emancipation statue should come down!" but over the circumstances of that statue and its particular portrayal.
The DC statue produced a fascinating debate on the site between opponents and defenders of it. That statue has been debated by African Americans since it was erected in 1876.
Another point too: Some people just don't like any statues. That's fine as a consistent point. Others don't want to take ANY statues down. That's fine too. But if you are in neither of these camps, be sure to explain why statue A should come down but not statue B.
And when deliberating over whether a statue should come down, be mindful that it likely has been part of the landscape for many decades with few knowing its meaning. It has gathered moss over time, its meaning removed from the thing it venerates and the time it was erected.
People often resist removing statues because they genuinely don't know why it was built. Take time to build community support for its removal by educating those who don't know. If governments infringe on community rights to decide, that's when direct action makes sense.
Final thought: Statues are about memory. Insofar as they are about history, they tell us about the moment in which they were erected. That purpose may make a particular statue worthy of preserving, contextualizing or removing. But that purpose should be considered in each case.