How do you clean cheesecloth?
For real cheesecloth, I throw it in the washing machine, with my clothes. It doesn't get sterile, but it gets clean enough that I don't worry about it becoming rancid. Rinsing it alone wouldn't suffice if you've been using it to strain fatty foods, like yogurt or cheese.

For the cheap "cheesecloth" that sold in the cleaning sections of grocery stores, that would shred to threads if you tried to clean it. It's cheap and disposable, so just throw it out.