Which branch of Islam allows drinking alcohol?

In Turkey most of the population are Sunni, which definitely prohibits alcohol (even indirect contact with alcohol, like people drinking it)

In fact most of the muslims in the world are Sunni

Only because people drink alcohol in Turkey doesn't mean that all Sunni in the world do it

Turkey is one of the rare Muslim countries in the world that went through a process of secularization where people are free to follow whatever religion they want and there are no laws prohibiting the selling of alcohol

For example during the Ottoman Empire there was a tax on alcohol introduced when many non-muslim people became Ottoman citizens - that tax was called 'tax on prohibited goods'

So people in Turkey are simply not following at 100% their religion and there is nothing wrong in that