"I'm not sure if you're aware, but you are chewing quite loudly"
Tone (neutral) is important. Sometimes they genuinely aren't aware. They know it's theoretically a social faux pas but never thought to check themselves.
I think they've grown up around loud eaters.
I've had nice conversations about it, the person listened, but was only able to be reasonable quiet for a short period of time. And then simply reverted. (they didn't care)
I found the best solution was simply to face this head on and deaden my reactions to it. This reduced my reactions to a living tolerable level.
Well, that's just you not empathizing with them. Chewing is not too different from walking. Imagine if someone told you they think your gait is too short, and could you take longer steps. How long would you be able to hold your affected gait before going back to your optimal gait?
Any subconscious behavior has to be controlled with a lot of effort and focus to change.
Almost no one I have ever met has changed a subconscious behavior, just because I asked in a certain way.
Walking can be met half way, or I can adjust _my_ gait to match there's. There's no equivalent to an irritating behavior.