I think you have 3 alternatives:
1. Create a Twitter account.
2. Stop using Twitter.
3. Use Facebook, Tumblr, or Mastodon for microblogging.
Twitter started requiring a login screen to view posts, but it's not the first website to do so. Pinterest and Instagram have done this for ages. We all hate it, but it's business.
I wonder why Tumblr isn't more successful than it is. It used to be a pretty well-known platform, and it's almost identical to Twitter, but while every celebrity seems to have a Twitter account, nobody seems to have a Tumblr account. Perhaps they do, they just don't tell anybody about it?
I wish Mastodon wasn't a thing. I believe federation is a terrible idea for normal computer users due to its non-obvious dangers, specially as more people will begin using Mastodon as if it were Facebook. I saw on Reddit that someone is building an open source, non-federated Reddit clone. That's what I think would have been better: an open-source, non-federated Twitter clone. Does anybody know of something like that, by the way?