Yes they are prohibited - anything that makes that much heat is (candles, coffee pots, hot pots, hot plates)
But that doesnt keep people from bringing, buying or using them. If you get caught, there might be some disiplinary action. If you cause a fire, then you're fired!
If you're in entertainment - most theater costume areas will have an iron and board somewhere. Most crew laudries have an ironing setup - but due the the amount of people using and misusing - 75% of the time they're missing or broken. If you're an officer - you usually get your uniforms cleaned and pressed for free.
I brought an iron for the first couple of contracts, but now . . . it's just added weight and I can always find one around. Buy fabics that don't wrinkle easily or look good wrinkled, like gauzes. It's better to wait to see if you really need on onboard, and then buy one in port if you really have to have it.