When I was young, young guys I knew drove around with car bodies in primer until they could afford the paint... Red? Gray? Yellow? (yuck) Long ago.
Now they prep the metal, then the pigment, then one or two clear coats... In a sealed booth where they wear breathing gear, 'cause the finish can get into your lungs and kill you...
You say "ordinary auto wax..." What, exactly, are you talking about?
I would worry that some of the "auto waxes" for today's super finishes might have something that could harm blue.
Now if you are talking about "furniture wax" or "wood wax" or
Shoe polish too. I would be much less concerned.
Many, many, for all my life have handled guns with a "tack rag." Rag impregnated with rosin or other natural resin. Keeps a light coat on metal and wood and hurts nothing. I wouldn't worry about bees wax either. Or lanolin. Little gooey. Castor oil. Oily.
Then there are the sprays. WD 40 is now the oldest and out of date. Silicon sprays. Lubes. Graphite. Moly. Chain lubes. I am not afraid to go over something with WD 40 lightly, but for better protection, yes, wax, but the modern finish car waxes... they scare me. Luck.