You can't access X without signing in, then there are the rate limits if you are signed in, but these things are not an issue with nitter. I went from checking Twitter as a logged out user every few days, to not using it at all after the access changes, to casually using nitter to check in on a few accounts I like.
https://nitter.net/search
https://github.com/zedeus/nitter/issues/983#issuecomment-168...
The required proxies are the reason currently only nitter.net is working, but not the other hosted instances.