This is one of those classic topics that there seems to be minimal science behind and everyone has their own opinion that they spout as the only truth!
Some say that light oil is all you need as 'spoke prep' and on the nipple heads as the wheel should be built correctly and using parts that are suitable for the weight of the rider.
Some say to use anti-seize. "I'm an aircraft mechanic and if it's good enough for a Boeing 747 then it's good enough for a bike wheel".
Some use (too much?) DT Spoke Freeze which I swear from minimal experience is just red Loctite. I bought a pair of used road wheels from a well regarded person in North Van years ago and he much have used that stuff as I literally couldn't turn any of the nipples.
Some swear by Wheelsmith Spoke Prep or boiled linseed oil. Both do largely the same job. Act as a lubricant initially then dry to 'gum' up the thread interfaces. DT Pro Lock nipples work in the same way too but with a two-part epoxy that gets mixed together when you screw the nipples / spokes together and then hardens.
To answer the exact question I think the concept of 'carbon safe' greases is a bit of a myth. All 'bike' greases are fine. Maybe there is some weird super toxic grease out there that will cause issues, or if people are total tight-asses and want to buy something off Ali-Express because everything you buy in a shop is a rip-off, then that might be a problem (probably not....). But a tube of grease lasts ages and is cheap enough.
Some people (including me in the past), drop a little Tri-Flow in between the rim and the nipple when starting to get to tension to lube the nipple head. It works but I find that the lube seeps out over time and leaves a wet mark around the nipple hole when dirty which doesn't look very 'pro'. I dab a little grease on the underside of the nipple heads.