Is it dangerous to publicly be an anarchist? Is it something that means I should be going above my usual levels of online security to hide?
It depends on what you mean by “dangerous.” You’re not likely to have a SWAT team kick down your door because you posted “anarchism is good” online, but you should still take precautions - just like how you should always mask up for any radical demonstration even if no laws are technically being broken. Not necessarily due to “danger” (though there is some amount of that, especially if you’re making real plans for real actions), but also because it’s just good praxis to not let your data be sold for profit. No one buying your browsing history is using it for anything good
The good news is, beefing up your security is generally not that hard. Just using Tor is a big step in the right direction, especially if you change some of your website choices too. You should also consider switching to Linux, which helps not only because it’s an open-source OS, but also because you’ll start using all the other open-source software designed for it. PureOS is a distro designed specifically for security if you want to take an extra step toward that, but something more user-friendly like Mint is fine too
As for your phone, Orbot and Orfox let you use Tor on mobile, and you can switch your messaging to the well-known Signal or the more obscure (but better, imo, since it’s decentralized) GNU Ring. Purism has developed a privacy-focused phone too, if you want to fully take the plunge, but if you can’t spare 600 bucks you can just get Ubuntu Touch instead (like I’m about to). Switching your phone’s OS is a bit more of a sacrifice (on desktop it only really affects gaming, and a lot of the time not even that), since most mobile apps don’t have support for those systems and the alternatives are a bit lacking, but for me since I do most of my phone stuff through the web anyway I don’t mind
Hope this helps! I’m kind of in the middle of doing this myself (except I’ve been using Linux for 4 years), so if you need help lmk and I’ll try to talk you through whatever problems you have