Earth's magnetic field deflects charged particles from the solar wind. Losing it would expose the upper atmosphere and technological systems to a different space environment.
What changes first
The atmosphere would still provide substantial protection from many forms of radiation, so a missing magnetic field would not instantly sterilize Earth. But the interaction with the solar wind would change, satellite operations would become harder and atmospheric escape could increase over very long periods.
The physical or biological constraint
The scenario should be treated as a thought experiment. Where the consequences depend on unknown parameters, there is no single precise outcome.