If you have a public account, you can turn off the ability for others to re-share your posts.
To stop allowing others to re-share your posts:
Tap
or your profile picture in the bottom right to go to your profile.
Tap
in the top right.
Below How others can interact with you, tap Sharing and remixes.
- Tap next to Allow post sharing to stories.
When this setting is turned off, users will not be able to do future reposts to their story.