What to wear
Three things will influence what you wear. The local culture; the weather and exactly where you are.
Egypt is a Muslim country. The culture and dress code are not as strict in Egypt as they are in some muslim countries, but it is still best to be modest, especially for ladies.
You may hear about some people who say they have been to Luxor and have worn exactly what they want, where they want, and nobody cared. The truth is that many people probably cared a great deal but didn't say anything. Just because they didn't understand what people were saying and thinking about them doesn't mean it is the right thing to do. It is much better to be sensitive to local culture and to dress in a way that will avoid offence.
Luxor is hot. Even in the winter, temperatures are generally high during the day so you will need light cottons at any time of the year. In some months, around October - March, it can get cooler in the evening and overnight. You can also feel the chill on a cruise boat and on the overnight train, because you get a breeze on the boat and they tend to turn the air conditioning to freezing on the train! So for any of these occasions, take a fleece or a jumper as well.
Men in Luxor
For men, what to wear is less of an issue than it is for women. Normal trousers and shirt, T-shirt or polo are fine. Make sure they are lightweight and natural fibres - cotton is best. Polyester or any similar artificial fabric will become uncomfortable very quickly.
By all means wear shorts in the hotel. Lots of people also wear them along the Corniche (the 'prom' beside the river) but most people would wear full length trousers in town. Luxor is a working ancient city, not a beach resort. Would you wear shorts in Athens or Rome? Certainly wear full-length trousers in mosques.
Women in Luxor
You will get away with wearing almost anything in Luxor, because the local people are getting used to seeing all sorts of things that are not really appropriate. But if you want advice on what is best to wear, rather than what you can get away with, then the advice is to dress modestly. Apart from the need to respect local custom and religion there are two other benefits from modest clothing. First, it will protect you from the sun. The sun is fierce most of the time and will soon damage exposed, unprotected skin. Second, the more modest you are the less attention you will attract.
A basic wardrobe would be loose cotton or linen trousers and/or a longish skirt and cotton tops with sleeves that are at least half-length. No-one expects you to cover your face. Nor do you have to cover your head. However, in the street you should not expose cleavage or thighs and preferably also cover knees and elbows. Clothing, especially blouses and skirts, should not be transparent or tight enough to describe your shape. Above the waist, baggy is best.
For something a little different, a cotton sarong is very versatile. They are cooler than trousers and you can use a safety pin to adjust the length to suit where you are or what you are doing. You can wear it short for the hotel or cruise boat, mid-calf when in Luxor itself and to your ankles for mosques and temples.
It is useful to carry a pashmina, chiffon scarf or shawl to help with covering up when you go to sensitive places, such as temples or mosques; to protect yourself from the sun, or if you find yourself amongst a group of 'admiring' men.
You will need 'practical' shoes. The roads and pavements are not tremendous (but improving in places) and to get to many of the sights you have to trample over unmade ground. Comfortable shoes or trainers with sturdy soles are best. Sandals are OK in the hotels and on cruises, but there is lots of sandy dust so they will become uncomfortable in town. When the coarse sand gets into sandals it can very quickly create blisters.
It is always necessary to dress modestly to enter a mosque. Some mosques have their own dress code that require more covering-up than the norm. This is where the pashmina or shawl comes in handy. Remove your shoes before you go in.
The dress code is much more relaxed on a cruise boat than it is in town. Dress as though you were in a tourist hotel. Shorts, swimming costumes, bikinis are all fine, but have something handy to cover up for when the ship gets to a town.
On four and five-star ships it is normal to dress up slightly for the evening meal. Few people would go as far as a tie for men or a long dress for women, and some people may go in shorts, but smart casual is expected. Shirt and full length trousers for men, and a dress or trousers or skirt with blouse for women.
Whereas Luxor is an ancient city with tourists, the Red Sea resorts like Sharm El Sheik and Hurghada are primarily tourist places and the dress code is much more relaxed. Shorts and T-shirts are fine for both genders but any form of nudity is illegal.
In the villages around Luxor or further afield, dress is much more conservative. There is no need to cover your face or head, but women will be respected more if they do wear a head scarf of some kind. Women should cover arms below the elbow, legs at least to mid-calf and chest at least to just below the neck. When travelling from Luxor to other resorts you will go through traditional towns and villages, so on the bus or in the car, be ready to cover up.
Cairo is a city where dress is modest and business-like. It would not be thought acceptable for men or women to wear shorts or vest-type T-shirts.
See also ....
Of course, exactly what you wear will depend on the weather. For more on the weather look at the weather page.
What you wear will be influenced by the local culture. There is more on the culture page.
For reducing health risks on the flights there and back, Sock Shop have a selection of flight socks for men and women.