Twitter is private from the point of view that matters at hand; that is, the legal one. Whether or not you can see content without an account has no bearing on this as this is a matter of ownership and liability. Even if it did, you cannot participate in those discussions without an account.

Laws pertaining to free speech do not apply here, as has been established time and again, partly because, like I said, it is their free speech in the wider gamut to remove things they don't want. Twitter's right to free speech exists in the public space, but your right to speech extends as far as Twitter's terms of service.

This all seems mostly disingenuous anyway -- the bias is very exaggerated. The right is mostly backed by armies of bots (a violation) and generally people who flaunt the rules more (anecdotally). Just something else to be outraged at.