Supposing governing laws allow you to race convertibles with the top down.
Would it be safe to race with a rollcage with a front rollbar along the A-pillars and windshield header in addition to the standard rear rollhoops the ones just behind the driver and passenger?
Something like
For mid-engine racers
And like
For front engine cars.
While the depicted rollbars block door access, Who needs doors to get in and out of a low slung convertible!