I’ve killed a lot of animals dead and without issue with push feed, off the shelf, rifles. To be honest, I didn’t know to ask or think about the difference until I got on AH. I don’t know it was a thing for a long time. Now, I realize I have several rifles that are CRF or a variation of. The OP stated his desire for CRF, so the assumption is he knows the difference and knows what he wants.
I have several REM 700’s and they work great, one does have an M-16 style claw extractor and it works great too.
I think my Winchester M70 in 300 WBY is push feed and it killed a lot of of sheep, deer, antelope, and elk without issue…
Hell, I used right handed rifles for years, even though I shoot LH. Now that I can afford LH rifles I want and my needs have changed, I’ll spend more money for value. And, I don’t feel particularly elitist about it… I’m not interested in wasting time criticizing others about their choices of rifles and/or gear. If it works for them and they can prove that it is effective by ethically hunting and killing game, then they should post first hand experiences so the members of this community can glean as much good as possible from it…
To each their own.