Sometimes when they approach you, you're up for a little street epistemology, Boghossian-style: how do you know what you believe is true, do you think faith is a reliable way to know the world, do you think people can believe things on faith and never know they're wrong, how do you know you're not wrong, would you be willing to change your beliefs based on evidence, etc.
Sometimes you're not interested and you just want to get your coffee/watch your program/masturbate in peace. Hell, you don't even need an actual reason. At those times, "no, thank you" is sufficient. No explanations, no excuses are required. "No, thank you." This is the end of the matter.
If they persist, the gloves come off. Anything after this is justified. My advice is not to give them anything. They're looking to engage you, to create or find an opening to continue on. Don't give it to them. They're trying to drag you into their pseudo-reality on their terms.
Remind them that you politely declined, and now they are being rude and disrespectful by ignoring your wishes, so they can kindly fuck off.
"Aren't you worried about your eternal soul?" No, I'm not. Fuck off.
"Have you heard the good news?" That you're going to fuck off?
"The [scripture] says…" I don't give a shit what your stupid book says, I give a shit about the fact I said no and you still haven't fucked off.
"What could be more important than getting right with the Lord?" What better things I might have to do are really none of your business, but right now you're keeping me from them so fuck off.
"Can we leave you with some literature?" No. I wouldn't read it and it would go straight into the recycle bin, so you and it should just fuck off together.
Make a point of noting their names, their church (or whatever) and the date and time, and advise them that their faith leaders will be getting a formal complaint. Now fuck off.
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