Drain tofu in a colander for about 5 minutes, then pat dry with paper towels.
In a blender or food processor, combine tofu, bananas, orange juice concentrate, vanilla, strawberries, and 4 tablespoons honey; whirl until very smooth. Taste, and add more honey if desired.
To quick-chill, pour tofu mixture into a bowl and nest in ice water; stir often until cold, about 5 minutes. Otherwise, cover and chill until cold, about 1 hour.
Pour tofu mixture into an ice cream maker (1 qt. or larger). Freeze according to manufacturer's directions until dasher is hard to turn or machine stops. Serve, or cover and freeze until firm, at least 3 hours. If sherbet gets too hard, soften in a microwave oven at half power (50%), checking at 15-second intervals, until it can be scooped, 30 to 60 seconds total.