Honestly, a former evangelical, now a full on atheist, but I have to say, in a logical standpoint.. belief in hell, and belief that you should mind your own business, seem at odds in a general stance. If you literally believe your god, views non belief as such a crime, that anyone following it deserves to be tortured for all of eternity, it logically follows that you should do everything in your power to convince them otherwise.
The concept of a you do you and not my problem is on par with say... being a die hard trump supporter, going out every week with "mass deportations now" signs. Then going out and grabbing a beer with your undocumented immigrant friends and saying to them "You're a cool guy, lets hang out until ice finds you and gives you what you deserve".