My first thoughts were far more logistical and practical....

What would I do with the soaking wet mama pad? If I didn't have anything to put the soaking wet pad in while I was still in the restroom stall, I may have been tempted to toss it in the trash. It would be due to not wanting my tiny purse soaking wet, though, not because of the "ick" factor!

Then, I was thinking, well I could dunk it a few more times (if the toilet was clean, like you wrote) to get rid of any excess menstrual fluid and squeeze it out, then put it in whatever item I would carry along if I did mama cloth. Then, it would be a little cleaner than usual, right? I'd wash my hands in HOT water with soap for a minute or more, but otherwise, I'd be fine. I wouldn't do anything different with the mama pad, I don't think....I don't use mama pads, though, so I cannot say for sure what I would do. My germ-o-phobe meter is pretty low, though, but some isolated things do spike it!
The thing that sticks out for me most, though, is I rarely see CLEAN public toilets. I mean, the facility is clean enough for a toilet seat cover use, but not clean enough on the inside of the bowl for me to clean willingly. I clean our home toilets with plain vinegar and don't think twice. They never get particularly dirty.