Toilet seats are very durable designs and most of them are made of some type of wooden composite from particle board to solid wood. Even padded seats are just a padded material bound to a wooden seat by either an adhesive formula or stitching. Because of their composition, a cracked toilet seat can be repaired if you so choose, and it can be done without any specialized knowledge and with tools that most any do-it-yourself person would own.
Remove the toilet seat from the toilet fixture by unscrewing the seat screws with a flat blade screwdriver in a counterclockwise rotation.
Spread the crack slightly and push wood glue inside of it. Many wood glue dispensers have a nozzle built into the container, and by putting the nozzle directly onto the crack, glue can be injected inside. Don't skimp on the glue, and make sure the entire inner surface of the crack is coated.
Squeeze the seat together using your bar clamp, exactly as you would do with any other wood project that is glued together.
Wipe off any excess glue that has been pushed out of the crack from the action of clamping the seat together.
Allow it to dry overnight, then remove the bar clamp and re-install the toilet seat in reverse order of removal.