On formal nights you will see everything from tuxedos and gowns, to pants suits and jacket and tie. They will not allow flip flops and shorts. I've even seen men just wearing dress shirts with no ties or jackets. Just wear something you would to a nice restaurant and you should be fine.
I do not think that RCCL would turn you away if you were not wearing a suit and tie. They will as Penny said turn you away or suggest you eat at another venue if you are wearing shorts, flip flops and the like. I have seen many people wear simply white or dark shirt and a pair of dark pants. No problem there. If you are trying to save space in luggage I would suggest black shirt and black dress pants and you will be covered for true formal and then semi formal nights and you will also look spiffy attending any of the nightly events at the clubs. I have mentioned many times before in various posts that dressing up can be an adventure and is fun. Why not take advantage of it.
We just got off a 2 week trip on the Vision. On formal nights we had people wearing Hawaiian shirts, sandals, and jeans. Nobody from RCI objected. I suspect that you could wear (within limits)casual clothes to any formal dinner.
While I agree totally that Hawaiian shirts and sandals are bad ideas on formal nights, I was stunned recently at how much some of those shirts can cost. There is a shop in Honolulu that sells vintage Hawaiian shirts. Tony Bourdain bought one on the show and paid $3000 for one shirt. The owner of the shop said Jimmy Buffet was a regular and had recently paid $4000 for a shirt.
I saw that too and thought it was absolutely absurd. Those guys just have more money than they know what to do with. A $25, $30 Hawaiian shirt with nice dress pants can look very nice. But sandals...tacky.
Yes, on casual nights for warm weather cruises I am often wearing a nice Hawaiian shirt and slacks, along with some loafers. It is a good look and it suits me well - and I think it is perfectly acceptable for a casual night in the Caribbean. Not so on a formal night.
Men generally shouldn't wear sandals except during the day or around the pool.
I think they should have directed them to the Lido Luau. At the minimum men should wear dress shirts and slacks with real shoes.
Not to drift too much here, but since the cost of Hawaiian shirts was mentioned. When Tommy Bahama's opened here last year I was lucky enough to have received a $50 gift certificate to try out the restaurant or use for merchandise. I figured I'd use it for a nice Hawaiian shirt for my cruise to wear on a casual night. Wrong! It might have gotten me half of a shirt if it was on sale.