No, Linktree is not banned from Instagram. In 2018, there was an issue where all Linktree links were flagged as "breaking community standards," specifically as a spam website. The ban was quickly lifted and Instagram issued an apology. That said, there is always a risk that Instagram could change its policy on Linktree links in profiles.
Mentioned in this answer
Linktree
Connect audiences to all your content with one link