Can a toilet be made quieter?

Under a cap at the top of the flushometer you'll find a screw. Turning that one way or the other will reduce/increase how long a flush takes, which might reduce the noise. Google the model number and details will turn up.

My contractor says all the flushometer models are so noisy because they're powerful. He said that people prefer tank toilets for that reason, but sometimes you have to flush repeatedly. I did have a water saver tank toilet in my last place that was so powerful that you'd think a jet was taking off. Some of the other neighbors had theirs taken out. Maybe there's nothing you can do if you want the power.

The power of the flushing is worth a bit of noise if you set the flushometer too much it will spritz up at the end of the flush cycle

I think c0lumbiac0unty had a noise problem with his outhouse, and so he just set up a system where the chickens would go at a different time than the horses.