A member of the Threads team just posted about it. I was able to log in from Chrome on iOS; on Safari, for some reason, I wasn’t. I’m assuming that whatever is going on there will be fixed sometime soon.
And even though I’m running into that issue, I’m happy that using Threads through a mobile browser is an option at all. I’m weird: I like to log in to social media services through the mobile web instead of downloading an app.