Does farting in the tub put me at risk for pink eye?

After a particularly gassy bath, I realized I splash water in my face/rub my eye/wash my face with the bathwater.

Baths relax me, and I'm assuming this is why I usually fart within the first bit of getting in.

Am I risking pink eye, or does the soap in the water neutralize the poo particles?

It hasn't happened before, but ive heard that you can get pinkeye if someone farts on your pillow. What other risks might we be taking without knowing?