I do the ironing in our house and yes, tea towels are ironed. The odd t-shirt of mine + summer dresses, quilt covers and pillowcases (sometimes sheets too) + I do his t-shirts, work stuff and jeans. If it doesn't need ironing I won't bother. In winter when I will put a fleece/hoodie over t-shirts I have been known not to bother and pull them out of the ironing pile as nobody will see them a bit creased anyway - as I rarely go out I don't feel the need to iron any more than I need to. Before anyone gets on my case for ironing a few bits that are not mine, there is a lot I am unable to do and he does all of this so I don't mind the few jobs I can manage - he has never asked me, never moaned if I haven't done it and often thanks me when he finds newly ironed bits in his drawers or wardrobe or even left in a pile to be put away by him. I also regularly thank him for all he does to help me too - it works both ways.
I have giggled at a few comments and hats off to those who don't or won't iron - I'm nearly at that stage! One of my ex-boyfriends had a mum who ironed/pressed/starched everything, including socks, underwear, flannels, towels etc - I still remember biting my tongue as a teenager that didn't get why these things needed ironing.