Starshield is like a private totally separate Starlink for the US government (and controlled/operated by the US government). I am not sure what sort of neutrality you were expecting as US government is SpaceX's biggest customer and is obviously a critical infra company.

I expect it not to be involved with the military, which was something they stated

Why would you assume any space company anywhere can be neutral to their nations military. These companies depend on government for far too many things (projects, permits) and are much more tied to government than other industries.

When did SpaceX claim they weren’t involved with military? They are launching military payloads all the time.

Starlink is as neutral as government regulations allow (both the US regulations and those of the customer’s country). They just want to make a profit.

Starshield is a separate constellation for the US government and select allies only, and is built and launched by SpaceX.

Starlink is neutral. Starshield is not. Starshield runs on different satellites with potential for custom additional payloads as well.