The best solution is not to cave to anyone. It's to come out, say what you think is best, then tell anyone who disagrees to either take it or leave the platform.
If enough companies, groups and individuals do that, this sort of pressure will stop, since people will learn it doesn't work. Most people won't stop using a platform over this stuff anyway.
In order to do that you have to go the Silk Road route, and try to host the site untraceably, paying for the server in Bitcoin, with the server hosted in a country with a no-extradition policy but has fast Internet. Otherwise for the platform to exist on the "regular" Internet, with servers and server admin living in a country with laws, the platform has to start policing content - banning the sale of drugs, weapons, and murder-for-hire, along with censoring other material - porn, gore, child pornography, copyright infringing material, files that are covered under ITAR.
The Internet is rife with censorship. It just offends our first amendment sensibilities to call it that for some very specific categories.
I wish it were that easy, but the things that keep people from shouting extremely distasteful but legal speech on every street corner of busy intersections don't really work for the internet, at least not yet. I suspect the only way to get a truly free and open honest platforms, is by removing anonymity and forcing users to categorize/tag their speech and then use punitive measures if they don't tag correctly.
Say you have a native feature where anonymous users or anyone will not see (by default) certain types of content by tags. The community might vote on which tags to require users to "opt in" to view. The only way to be banned might be, assuming legal speech in the first place, would be if someone posts content that fits within a community agreed upon tag, but the user fails to tag it.
I haven't given this a ton of thought, but I would love to see something like this tried.
If enough companies, groups and individuals do that, this sort of pressure will stop, since people will learn it doesn't work. Most people won't stop using a platform over this stuff anyway.