Protocols (not templates) can be edited by people that have the role of an Owner or a User at the project level.
If you want to edit a protocol template in the Protocols repository (see the image below), you need to be the creator of the protocol template.
If a template is stored under the Protocols repository tab, other team members can create a copy of it, save it with another name and make changes to it. They create their own copy.
If a template is stored under the My protocols tab, other team members cannot access it. However, the creator of the protocol can convert a private protocol to team protocol and make it accessible to others.
To learn more about how you can edit a protocol with the Protocols repository, please see the video below.