Banning twitter posts would be asinine. Hexbear already tried to do that when Elon bought twitter and it failed.
This is because many news agencies, journalists, public figures, and even governments post new information on twitter before any other website.
A twitter post is good as long as the hexbear post gives a link to the tweet and the tweet is from a reliable twitter account.
The worst posts on hexbear are the reposted images and videos from reddit without verifying that the material is legitimate or linking to the original source.