Can I set fine-grained path access controls in the Subversion repository?

No. While corporate software projects tend to revolve around fine-grained access control to source code, we don't think that this is the most productive practice for open source development. In an open source project, the code is entirely public and the developer community should be based on trust. If your community invites someone to be a project member, then it's a collective statement that your community trusts the person with write access to the repository. If the community feels that the person should only change certain portions of the source code, then that expectation should be made clear. If the new member violates this social contract, the community is free to expel the member and revert any unwanted commits.