By being polite and firm.

Good to hear that your father came through - hope he's continuing to do well

When my brother-in-law was killed, we had him buried in Arlington, requesting an agnostic service. The Chaplain who officiated did a very good job, and I was so impressed at his willingness to take our hands, shake them, and acknowledge what a painful day that was for us.

I would feel even more ill after a visit from a 'holy' man.

Some chaplains are trained in multi-faith spiritual care, even familiar and understanding of humanistic values. So, not all chaplains are dogmatic fire and brimstone types.
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When my daughter was recovering from surgery (as a minor) I was in the room when the chaplain came in. I explained that we were firm atheists, so I didn't think the chaplain could offer much in the way of spiritual care for us. The chaplain said she completely understood and that she did have some experience with humanistic chaplaincy, and to let her know if she could be of any help to us. I was pleasantly surprised by her comment and thanked her for that.
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I have actually considered training to become a humanist chaplain for the growing number of "nones" who might need some humanistic support while in hospice or recovering from illness in the hospital.

"Thank you for your concern." And turn away.

If he says, "I'll pray for his recovery," you can then say, "Whatever."

I agree with everyone else here. Just politely say "no thanks." End of discussion. I think they are there more as a service to believers than on a mission to convert new followers. They should take no offense to being declined by nonbelievers.

Good for you

"We won't be needing your services, thank you." Any further attempt would result in a much less polite response.

The priest or chaplain (usually there are several religions on-call around here, Never appears unless requested.

Just say ‘No thanks, I’m with the other guy”. Point down and wink. He’ll soon go away. Lol

"No thanks."

Not had that experience yet but the way I see it I that situation you can be as rude as you like you ha e a lot more things to be worried about than that leeches feelings ....I hope your dad feels better soon

Just say no thank you.