I should think the modern day safe equivalent would be something like a graphite based one or copperslip . But it gets everywhere, you only have to look at it and you are covered in the stuff.
When turning between centres I use a general purpose grease, and have got away with it up until now. Modern formulations have come a long way over the years, and as long as it doesn't melt out due to friction heat, I think it would be fairly safe to use.
John