I believe in some of the Atlas literature the recommendation was a graphite grease but those are not so easy to find these days. I did get some from the UK a while back and that’s what I use.
However, there are many that will argue that grease is prone to swarf and chips getting stuck and thus embedding in the gear teeth, so they say a heavy or tacky oil is better. I’ve done both — the oil works fine but you need to apply it more often and it slings all over the place. Atlas machines are oily little critters at best, so adding to the party isn’t really what I wanted to do so I stick with my grease.
I sincerely doubt you will have any problem using your red grease. As said above, much is personal preference and what happens to be available or on hand. Anything is better than nothing.