Can farts spread diseases to other people who inhaled the farts?

Definitely, yes.: If they inhale your farts directly from your anus, in close proximity, intestinal bacteria can be transmitted. It has been shown that flushing toilets can distribute E. coli bacteria around the bathroom and end up on toothbrushes. If you can time your fart with your victim's inhalation precisely, and make sure that they were inhaling close to your bare anus, you might make them sick. Fun fact.