Would a flight consisting of solely first-class passengers be cancelled due to center-of-gravity issues?
It is much more difficult to load a plane so that the center of gravity ends up being too far forward than too far aft.
Excessive weight forward can almost always be counteracted by increased trim on the stabilizer.

When small GA planes crash due to Balance, its almost always too much rear-weight, not too much forward-weight.

Especially in the case you describe, the pax probably have luggage, and the luggage can be loaded in the rear of the plane for balance.