The best way to do this to keep a copy of your tree on your own computer and/or another website that isolates individual trees. You see FamilySearch Family Tree is one single tree, where everyone is linked together. If you and I share the same great-grandfather, he would only exist once in FamilySearch Family Tree and we would both be able to go up our direct ancestors to the same great-grandfather.
That said, the best way you can prevent others from adding incorrect information to individuals in FamilySearch Family Tree (I'm assuming you are researching and making sure the records and information you add is correct!) Is to give good reason statements, mark similar individuals as Not-a-Match, and write up a life sketch for them that clarifies any unusual circumstances and incorrect information from sources. The more you explain why you add sources and why certain information is correct, the less likely other folks (especially inexperienced ones) will change your information.
Family Search is NOT a system (like Ancestry) where everyone has their own private tree
The FamilySearch system is based on a single collaborative database that we all share and contribute to. Learning to work together is critical in your success using the FamilySearch Family Tree.
If your goal is to have a private family tree that you have total control of - you are best using other products - such as standalone family tree applications like Roots Magic or Ancestry Quest.
But no matter what your choice is - I highly recommend watching this video:
WHY USE FAMILYSEARCH FAMILYTREE
FamilySearch is a world tree so anyone can come along and mess up your work. I recommend clicking the Follow star and once a week you'll be notified of any changes made to the individuals you are following. I also recommend you keep a copy of your family in a program that only you can edit such as Ancestry.com (subscription based) or RootsMagic (free version is available).
Finally, on the right side of your person's page there is Latest Changes, click show all and you can see all the changes that have been made including merges in case you need to undo them.
https://www.familysearch.org/wiki/en/GEDCOM and https://www.ongenealogy.com/how-to-export-a-familysearch-gedcom-with-rootsmagic/
. . . we tend to not use the phrase "my tree" in FamilySearch - it implies ownership.
The database is a shared resource to all users. It is not Mine nor Yours.
It is OURS. a database of the world family - that we all contribute to.