When a political movement is begun through sympathy for violent criminals, I don't think it is a legitimate one. Certainly not one that should be given a public voice through our taxpayer dollars. Even if you think they should, should a public meeting be exclusionary and anti-white? If a hateful group like the Klan got together to discuss how they advocated violence against and hated a group and would only allow other Klan members to enter a public area, no one would have a problem if the library didn't allow them to hold an event that bars other people from entering a public space and promotes violence. Therefore, BLM also shouldn't be given a taxpayer funded platform to push their idiocy advocating violence against police and white people. If they want to assemble peacefully and not advocate violence or be violent, that's fine. But that is not what the current movement is about.
The library is publicly funded, so I definitely understand the reasons to prohibit these meetings. If white people are not allowed at the meetings, then the library should be able to ban them. I don't understand the reasoning behind Black Lives Matter not allowing white people. I think it would be a good idea for them to include white people. Having said that, I can't help but question the library's motives. I think there's a decent chance that fear and racism played into the decision, at least on a subconscious level.
If the Nashville Public Library has any concerns that any meeting may result in disruptions to the operation of the library, then I believe it is fair for them to prohibit Black Lives Matter meetings. The library is not an appropriate venue for such a large and vociferous gathering of people.
I mean, not one can really stop them from prohibiting whatever they want on their premises, but all it does is make them look bad. Despite what the media tries to sell, Black Lives Matter is a haphazard organization of harmless college students and intellectuals. All trying to silence them does is make them grow louder, and justifiably so.
If a public library has meeting space, then it is their responsibility to provide fair and equitable treatment to anyone seeking to use their space. It is not right for a public space that is funded by the taxpayers to be cut off for biased reasons. If it was a private space, one would likely be within their right to prohibit Black Lives Matter or any other organization. In this case, the public needs to make sure it applies the rules fairly.