You mean the twitter app? You can create a fake identity - the only info I had to give them was an email address (used one of the free email providers and an account I use for this kind of thing), and a "name" - also fake. That was for an account set up in a browser on a computer. To use the phone app, you may have to give it a mobile phone number (or use the browser on your phone instead of the app)...
Or are you talking about the app permissions? (I went and looked, and while you may not want to give them all that access, it's reasonable and necessary for the app to do what the app is designed to do.) There are lots of third-party twitter-related things, perhaps you can find one that's just meant to let you follow other people without having all the other stuff - some sort of twitter "feed" app.
Anywho, you can always just point your browser to
https://twitter.com/ldschurch without any kind of twitter account and see what's been posted. (It'll prompt you to get a twitter account, but just cancel that.)
FWIW,
Liz