If you're not wearing respectful clothes, please don't enter.
"Si prega di usare un abbigliamento adeguato alla casa di Dio. Pertanto si invita a non entrare in pantaloni corti, in minigonna, in canottiera, con la schiena scoperta o con abbigliamento troppo scollato. Grazie!"
Roughly translated: "Please use appropriate clothing to the house of God. Please don't enter wearing shorts, mini-skirts, in a singlet, or with backless or low-cut clothing. Thank you!"
Jeff's tranlsation: Wear modest and respectful clothes, for goodness' sake! God is here!
(These signs are everywhere in Rome... and you will get kicked out of Church if you're wearing the above mentioned clothing items. FYI for any future tourists).
Would you wear shorts and a tee shirt, or something you'd wear to a bar with some friends, when you go to meet the President of the United States? Now, it's one thing if the President were to pop in unexpectedly... you wouldn't be expected to dress your best at that time. But if you are going to a great feast with the leader of your company, country, state, etc., you're going to dress in nice pants and a dress shirt—at a minimum. Why can't you dress up for your God... the guy who created you and holds you in existence every moment of your life!?
It's hypocritical, in my opinion, to believe that the God of the universe is present inside every Catholic Church, and to not respect this fact. Are there exceptions to the rule of nice clothing inside a Church? Of course. I admit I've been to Mass in shorts once or twice (always when I didn't have time to get back to the house and get dressed), and I've often dropped in for a quick visit while wearing sweats and a tee shirt... but I wouldn't ever willingly wear what I wear while I'm strolling around the park or playing a round of golf in the summer to Holy Mass.
Please: dress with dignity. And dress nice for Jesus!