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You seem like you've been on Geni for a few years now. It's purpose is to create one World Family Tree so family can collaborate together on a single connected tree instead of everyone maintaining only their own copy of a family tree.
Once a profile is well sourced it can become a Master Profile on Geni. Master Profile is a designation that the profile is complete and accurate. When a duplicate is merged with a Master Profile all of the data stays as it was.
All profiles track their changes. Just look at the revisions tab to understand what has changed, and who made the change. Having revisions makes it easy to fix mistakes. We are human after all and mistakes can happen.
If the Master Profile designation and revision history isn't enough, Curators can mark a lock individual parts, or the whole profile if needed.
@Johathan Scott Krengel: Do you want a World Family that is totally incorrect - that is what it is NOW! These people have NO business changing or merging files to my dad's side of the family when they are only related to him though marriage (if that) when our trees were quite accurate according to OUR research that took many years!!! Also, they made a change to my husband's brother's name! Why??? Trust me they are NOT related to him at all! Yes, people are human but they don't have to be stupid and careless, as well. Do you accept that??? So very wrong to mess with information they know nothing about!!
Private User Thank you for the information about making it private. I will have to pass this on to the family. This is so sad that people can do this! So very wrong. Thank you, again. I appreciate you.
Private User - making a Profile Private might not solve your problem. If someone is in one's Family Group they can edit all Private Profiles where one is a Manager - does not matter whether the profile is on the same side they are related on or not.
If you feel someone is purposely vandalizing, you can report them and if it is true, then they will likely be kicked off Geni. But sounds like these were more likely stupid than malicious.
Geni relies on people to correct any errors, They notify managers and those following a Profile when a change is made to it -- they do that so those folks can look and fix errors.
You mention "our trees were quite accurate according to OUR research that took many years!!! " -- How have you documented that research on the Profiles?
Have you uploaded Documents to the profile? Do you have comments in the overview?