I wish I had known what the real requirements for clothing were before we went. We went in late May/ early June and the weather is warm. Reading the information ahead of time made me think men needed long pants and women needed long pants/skirt and covered shoulders in a mosque or religious setting. So we packed more than usual and even purchased clothing that would be appropriate. As it turns out, our guide told us that shorts and sleeveless shirts were fine. The only requirement was for women to wear a head scarf. We did not wear short shorts or revealing tops, but we could have saved a fair amount of packing space and some money as well.
When I was in Turkey, about 10 years ago, I noticed that as a group the Turks dress modestly. I did not see many Turkish men wear shorts and sandals, even in hot weather. Light pants and shoes were the order of the day. Women dressed fashionably, most with scarves but not all. However, tank tops, halter tops, shorts of any kind, tight fitting clothing were not worn by Turkish females. Not at all. Several female members of our group purchased the voluminous Turkish pants a lot of the older women wear. They found them comfortable in the hot weather, and they were a conversation starter with more than one native.
OTOH, they are used to tourists wearing shorts and sandals. Just make sure the shorts are not too far above the knee. It's not Saudi Arabia, and it's not a beach in France either.
It depends on where you are in Turkey. When I was in Antalya in May, I saw everything -- shorts on women and men, wispy sundresses, tank tops, tube tops, etc. In fact, looking at my pictures from the trip, I would say that shorts were the norm, especially among tourists, but sometimes with Turkish men, too. (I didn't see any men in tank tops.) Nobody batted an eye.
In more conservative areas, like Konya, people dress more modestly, and I think it would be culturally considerate to stay away from shorts and tank tops.
It may be that things have loosened up in the last 10 years, but even in the RS videos from over 10 years ago, Lale was wearing a sundress. My point is that it's not necessary to buy special clothes. Somewhat modest long shorts were appropriate for the warm weather.
We would never dress in a way that was disrespectful, but on the whole Turkey is much more relaxed than say, Jordan, where our (men and women) legs were covered all of the time, unless we were at a resort.