I never iron my underwear. In fact, I stuff my underwear into a drawer without any folding, just a big wrinkly heap. Whereas my partner carefully rolls all his underwear, reminding me of our enlisted days in regulation Army barracks. I think it's a waste of time. If anyone sees my shorts at the gym, they'll be wrinkled from wearing anyway, whether they were carefully ironed before or not.
On the other hand, I do iron, or have professionally pressed, any outerwear when going to someone's house for dinner or cocktails, or some kind of function or reception. In fact, I'll often hang my shirt in the car, wearing a T-shirt while driving, and not slip the outer shirt on until after arriving, to avoid seatbelt wrinkles.
And if it's formal, I'll likewise not wear my dinner jacket until I arrive and step out of my car, so it's totally wrinkle free. I must admit I do disdain men who are a wrinkly disaster, when the occasion requires otherwise.