When a tree is synced from Family Tree Builder to the online Family Site, it can be viewed online, and edited by the site creator. It can also be edited by your site members if you have set the tree setting for it to be edited by your site members. You can edit these settings under Family Tree > Manage Trees > Edit tree settings.
As always, you have full control of who can view or add information to your site.
To edit those settings, please see the following post:
Family Tree Builder trees are meant to be synced to a family site and can be best experienced by syncing.
If you choose not to sync, there are a lot of features that you won’t be able to fully enjoy within the program, such as Smart Matching, Records Matching, Upcoming Events and Profile page from the Family Site section and more.
Syncing also serves as an online backup of your family tree. In case the tree on your computer becomes corrupt, you can easily download your family tree from your online family site. This is an invaluable part of syncing that protects your hard work.
You can choose to keep your family tree only to yourself, and to not sync it to your online family site.
To turn off Automatic Sync, please see here: How do I disable the Automatic Sync in Family Tree Builder?