I have no problem saying "Rest in Peace". I won't say that 'I'll send prayers', but I will say 'your in my thoughts'. I'll offer my condolences and respect.
I also say gesundheit or bless you (though I do feel silly) when someone sneezes. And I wish people a happy St. Patrick's Day and Merry Christmas, even though I don't recognize 'Saints' or 'Christ'.
I have no issues with the simple things that express some sort of concern or well-wishes to someone else.
It's a little difficult to navigate the word as an atheist when Christianity is so engrained into societal norms.

They're culturally vestigial. It has limited meaning. Goodbye is a contraction meaning god be with you. Should we stop saying goodbye?

Absolutely not. It's a prayer. And the alternative to resting in peace is burning in hell (like hawking is now according to the xtians). I'm not part of that.

The athiest god will strike you down if you do!

I stopped saying it because I feel it's pointless.

Perhaps there could be an atheist version to reflect what really happens after death? RIP - Rot, Insensibility, Putrefaction.

It does bother me some, but it's better than any other religious platitude. Sometimes I think the expression may have originated due to the fear of ghosts or vampires.

I never thought of that as a religious statement or a reference to afterlife.

You got no fucking choice but to rest in pease because your dead

Just what we need, the PROPER PHRASE POLICE........They're dead, say something comforting to the family ferpetssake.

My go to response to someone dying is "So sorry for your loss" and/or "My deepest Condolences"

Agreed we should change it to RIP. Rest in pain.

Why can't we live in peace? Now that would be nice!

I think it's ok to say, it's more a mark of respect and closure (for me at any rate) For example, if a celebrity or music star I particularly admired has died I would post a Youtube link on my Facebook page with RIP Joe Bloggs.

I see your point. However, in lieu of anything else that sounds better, it's nothing more to me than an inoccuous platitude. The believers are being pandered to by far worse than me, whenever I say that.

It is a meaningless phrase that most peole say because they can not think of anything better to say and is accepted by society.

Well, there's this alternative:

I just think nonexistence is a good form of being peaceful. No more suffering or fear, because there's no "insert person here" left to experience it.

It's just a made up phrase the living say to comfort the living

They are ritual words, nothing. A traditional way of saying you're sorry so and so died. So it doesn't really matter.

It;s just a way of speaking No mental activity required.

Would "remember in peace" be to wierd...

Its personal. I have not said that to anyone.

I have no problem with RIP. There are physical remains, be they ashes or a body, and also the memory of the deceased held in the thoughts of those who remember him/her.

Here in Hawaii, ashes (or cremains) are often scattered in the ocean or on a lovely vista. Folks often say "Rest in Paradise" with Paradise referring to Hawaii, not a supernatural heaven.

I hope memories of me rest peacefully in the hearts of those who have come to care for me and wherever my kids choose to have any remains of me is a peaceful place.

I don't think it's bad to say. I have been dead. It was blissful. Rest in peace to me means, your fight is over you may lay down now. It doesn't necessarily mean "have a good afterlife". I prefer it to "well poof you gone!" Or "you're in a better place".