Thats like saying banning facebook messenger hurts first amendment rights. It doesnt, I can simply use another app that is the exact same thing.
Google, Facebook, etc all do that, and it's their entire business model.
The government has a long history of regulating the transmission of speech. The First Amendment protects us against them regulating the content of speech.
For example, campaign finance laws dictate who can fund speech in certain situations, but they don't dictate what a candidate actually says.
That said, the First Amendment is limited by "compelling government interest," so there are no absolutes. We are, as we have been for a few centuries, at the mercy of the whims of the Supreme Court. There are no absolutes, and the Supreme Court can interpret anything however they want.
Banning 1984 would violate the First Amendment because it would be banning a certain point of view. Banning TikTok is about preventing a foreign government from owning an information pipeline, not about the point of view that's being pushed on it.
Anyway, all the people who claim to be concerned about the First Amendment should be marching in the streets over what's happening in Florida, not trying to save TikTok.
Its like if there was an e-reader that sat in your living room spying on you, but it displayed books for free. Banning that device is not the same as banning content itself.
I don't think they are about civil liberties in general any more. It's more they advocate for some civil liberties they currently support.
Facebook and Twitter are not constrained by the First Amendment. The First Amendment exists as an umbrella under which they can do whatever they want.
In this case the federal government (which is constrained by the First Amendment) is the one proposing to ban an app—entirely. That is most definitely a First Amendment issue.