The interactions between the Ottoman and Mamluk courts had a long history before the Ottoman conquest of 1517. Cairo was an important centre of learning where many Ottoman religio-legal bureaucrats visited in search of knowledge, craftsmen from Mamluk lands found employment in pre-Ottoman as well as Ottoman Anatolia, and artifacts including textiles were exchanged as gifts between the two courts. Ottoman visual arts developed in dialogue with the Mamluk world, as well as the Timurid/Turkmen courts in the east and Europe.
It is difficult to assess the impact of the Ottoman conquest on the textile industry in Egypt, as the Mamluk textile industry had its peak under private patronage in the fourteenth century but then saw a sharp decline by the early fifteenth century, long before the Ottoman conquest. There was, however, a thriving rug industry in Egypt which continued after the conquest. Interestingly, rather than the Mamluk rugs with geometric designs changing the taste in Istanbul, the Cairene workshops adapted themselves to the prevalent Ottoman taste and started producing carpets with floral designs in the mid sixteenth century. This is not surprising, given that this was a period when taste was quite heavily influenced by the Ottoman court workshops, as designs made by court artists in Istanbul were applied onto various media including textiles, tiles and rugs produced in semi-independent workshops outside Istanbul, which also catered to civilian customers.
The Ottoman author Gelibolulu Mustafa ‘Ali, writing in the late sixteenth century, highlighted how different the manners and costumes of Cairenes were as opposed to what he was accustomed to in Istanbul. One way of comparing costumes worn in different cities of the Ottoman empire would be to look through costume albums made from the sixteenth century onwards. Differences in costumes depicted in Ottoman manuscripts produced in Istanbul, Aleppo and Baghdad may also give clues. Yet unfortunately, we will probably never know what most people really wore in the sixteenth century, because apart from royal items kept in museums, the garments themselves have not survived.
Some sources where you might find answers to this question:
Bethany J. Walker, ‘Rethinking Mamluk Textiles’. Mamluk Studies Review 4 (2000), pp. 167–217.
Gwendolyn Callaço, ‘Dressing a City’s Demeanour: Ottoman Costume Albums and the Portrayal of Urban Identity in the Early Seventeenth Century’. Textile History 48 (2017), pp. 248–267.
Suraiya Faroqhi and Christoph K. Neumann, Ottoman Costumes: From Textile to Identity. Istanbul: Eren, 2004.