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Probably limited a small bit by structural strength, i.e. more acceleration means a stronger and heavier structure. For manned rockets, the G forces are even lower to accomodate the astronauts. So I'm assuming that even lower accelerations are only possible if you trade off fuel efficiency.
Astronauts normally experience a maximum g-force of around 3gs during a rocket launch. This is equivalent to three times the force of gravity humans are normally exposed to when on Earth but is survivable for the passengers. Astronauts are trained in high g-force, wear g-suits and must be correctly prepared.