I can't share the experience with OP as I have a longstanding reddit account and really only participate in niche subreddits using old reddit. My rule of thumb is to always be skeptical about ban grievance stories that don't provide all the details that a knowledgeable person would ask. What, precisely, was posted? What platform was it posted from? Was there a dancing around of IP addresses and estimated locations with VPNs?

If I were to make a new account, I'm wondering if I would run into the same issues. Surely it can't be that difficult for new users to join reddit?

There's a separate, larger discussion about aspects of the modern internet that people are going to have to get used to, in that "determining whether someone is a real person or not" will be necessary for a lot of services to stay alive. I don't believe the conspiracies that attempts to do this are all for mass surveillance. Mostly, a place for people to talk can only live if people trust that they're talking to other people. Right now, we're seeing some botched or overzealous implementations of this, which might describe what OP ran into.