Is it possible for religious Muslim to do business on Friday?
Is it okay according to sharia to buy clothes on Friday?
I know Christians (mostly) are allowed to do so on Sunday and Jewish aren't allowed to do so on Saturday.
Yes. What is forbidden is doing something after the calling for Jumu'ah prayer and before the end of the prayer. Doing anything, including business, before and after this time is permitted.
يا أيها الذين آمنوا إذا نودي للصلاة من يوم الجمعة فاسعوا إلى ذكر الله وذروا البيع ذلكم خير لكم إن كنتم تعلمون فإذا قضيت الصلاة فانتشروا في الأرض وابتغوا من فضل الله واذكروا الله كثيرا لعلكم تفلحون
O you who have believed, when [the adhan] is called for the prayer on the day of Jumu'ah [Friday], then proceed to the remembrance of Allah and leave trade. That is better for you, if you only knew.
And when the prayer has been concluded, disperse within the land and seek from the bounty of Allah, and remember Allah often that you may succeed.