President Trump is not what you'd call a free speech advocate. He's been pretty open about his desire to `open up' US libel laws to make it easier to sue news media outlets.
Now, he's blocked dissenting Twitter users so they can't follow @realdonaldtrump, read his tweets or otherwise interact with his Twitter account. The blocked users decided to sue him under the US First Amendment free speech protections.
The First Amendment basically says that the US government can't make a law abridging freedom of speech. US courts have interpreted this to mean individuals have the right to express themselves without interference by the government.
The degree of protection depends on the speaker's forum. Public forums (think parks and footpaths) get the strongest protection, and the government can't discriminate against people in public forums based on their views.
The case against President Trump claims that his Twitter account @realdonaldtrump is a public forum. Interesting question; whether a Twitter account could be a public channel for communication between the government and the general public.
The account obviously represents statements from President Trump, and they're available to the general public (unless you're blocked). Although there is a separate, more official looking @POTUS account, Press Secretary Sean Spicer has stated that @realdonaldtrump tweets are "official statements".
A key issue is likely to be whether @realdonaldtrump's feed is a place of public interaction, rather than just a one-way Presidential communications channel. If it's the latter, then it's not treated as a public forum and the Government need not be viewpoint neutral. Notwithstanding Sean Spicer's statements, we're not entirely convinced that tweets like this could truly be labelled "government" speech.
"With all of its phony unnamed sources & highly slanted & even fraudulent reporting, #Fake News is DISTORTING DEMOCRACY in our country!"
If Trump loses, he'll have (involuntarily) contributed to an expansion of free speech rights in the US. Wouldn't that be a sweet irony.