That's a complicated question.
I'm going to make an assumption that, for your purposes, you most likely don't have anything to worry about, but still:
Does participating in an online community about anarchism out you on a watchlist? There's no way to know what precisely constitutes a "watchlist" or what criteria US intelligence agencies use to populate them, but we do know that the DOD considers anarchists an "extremist ideology" that constitutes a potential "internal threat." Public communications and documents from US agencies indicate that "anarchist extremism" and/or "anarchist violent extremism" is a threat that is being monitored by law enforcement and intelligence agencies.
To address the question of violence, we also know that certain methods of surveillance by the US government are notoriously broad, and are not predicated on the commission of a crime, so it's not unlikely that simple suspicions of anarchist extremism could land your data in an NSA database somewhere. However, your data on an NSA watchlist is very unlikely to get you arrested if all you do is talk about the ideology and don't make anything that constitutes a threat of harm. And you're probably in that database anyway for some other reason.
Can you get arrested/charged for crimes? Not to be hyperbolic, but police can arrest you and charge you with crimes for any reason at any time. There's nothing you can do that guarantees you won't ever be arrested. That being said, being arrested and charged does not mean you'll be convicted, and police don't have infinite resources to just arrest anyone and everyone forever.
Still, are there examples of anarchists who have been spuriously arrested and charged with crimes despite being nonviolent? Yes. I've been arrested for nonviolent, legal political protest. I wasn't breaking any laws. I spent a day in jail on a made up charge, then they released me and never pursued the charge in court. Just a scare tactic. That's not an unusual story.
For a more extreme and recent example, anarchists in Atlanta are being charged with domestic terrorism, and one of them was extrajudicially murdered, for their nonviolent protests to stop cop city. Organizers for the legal, nonprofit bail fund in Atlanta were also arrested and charged spuriously with money laundering and charity fraud in a related case.
Two things about those incidents, though. One, these arrests are by local police with a grudge, and so I doubt it's related to a federal watchlist. Two, the victims are actively engaged in organizing for a political protest movement, not just chatting about Bakunin and Proudhon on a forum.
I think you should get involved, talk, and learn more about anarchism, socialism, communism, any stripe of anti-capitalism. I'm confident that you can learn about it and chat about it safely, regardless of whether your data ends up in an NSA database. But you should be aware that getting involved in IRL organizing on the left, even nonviolently (as it almost always is), isn't safe. It's absolutely, 100% worth doing, but political resistance has never been safe, and part of a good education is learning how to protect yourself.