Running an LLM locally makes no difference at all to the threat of malicious instructions that make it into the model causing unwanted actions or exfiltrating data.

If anything a local LLM is more likely to have those problems because it's not as capable at detecting malicious tricks as a larger model.

This is the MCP problem, essentially, and the solution is the same: the user should review and approve specific actions before they are taken.

Of course there will probably be a setting to auto-approve everything...