When in illustrator, a file set to RGB with our hex number looks as it should, of course. When I convert the doc to CMYK for printed materials, the program automatically converts the color and the hex number changes as I expect. However, the CMYK values do not match our guideline. When I correct the CMYK values, the appearance of our orange changes and looks terribly like the wrong color. My question is - should I let illustrator convert the RGB automatically, which produces a good looking color with incorrect CMYK values. Or should I always use the correct CMYK values even though the color looks wrong? 

Hi - I've attached an Illustrator course to this thread ['More Info' at the top] -- there are a couple of sections on exporting, maybe one of them will help..? https://www.macprovideo.com/course/illustrator-301--advanced-techniques?afid=E470KLQ7r9 I can't advise [I'm from the music/audio side of things here], but hopefully an Illustrator expect/guru will be able to offer some guidance.. Off the top of my head though, is there any way to export the material both ways, and see which works, or is it a situation where once it hits print it's too late [no way to do a test run]..? Just in case, here's another course that includes sections on color, in case there's anything useful in there: https://www.macprovideo.com/course/diving-deeper-into-illustrator?afid=E470KLQ7r9 I also came across this Adobe Help page -- maybe there's additional stuff there that addresses your issue more specifically.. https://helpx.adobe.com/illustrator/using/color.html