You do not have the right to follow the President on Twitter
I have been blocked by both Twitter accounts maintained by Planned Parenthood of Indiana and Kentucky. Despite the fact that PPINK is awash in tax dollars, my First Amendment rights are not violated by being blocked. The fact that I am blocked does not prevent me from following them on Twitter, of course, since I can use private browsing to follow both of PPINK's accounts.
In the same way, President Trump's critics are in no way deprived of their First Amendment rights when he blocks them on Twitter. They can still easily read his tweets through private browsing or setting up an alternate account - and it is a simple matter to switch between accounts on a phone, a tablet or even a desktop computer by using things like Twitter for Windows or Tweetdeck.
So why the lawsuit? Someone on Twitter made an excellent point. The people suing Trump are not bothered by being "unable" to follow him, because they can follow him easily. What they want is the prime real estate below Trump's tweets to make their own profiles more visible. They are not denied access to Twitter and can still criticize the President to their heart's content - provided they follow Twitter's Terms of Service Agreement. No one is being denied the ability to read what they want, or the freedom to write what they want.
It is absurd to argue that a private social network is subject to the First Amendment. This is a fake controversy that only exists because so much of our culture is consumed with a victim mentality. The courts need to dismiss this lawsuit for the frivolous nonsense it is.