بسم الله الرحمن الرحيم
It is haram and unlawful and major sin to shave the beard or keep it less than one fist. It is also not correct to cut the hair differently in length as per the English style, it is makrooh tahrimi. So the barber who avoids haram things in his profession like shaving beard etc his profession and income is lawful and one who does not avoid it and shaves beard or cuts it less than one fist then his profession is not lawful and the income which he derives by shaving the beard is not lawful and halal. It is mentioned in Tabyeen Al-Haqaiq (5:125):
ولا يجوز على الغناء والنوح والملاهي لأن المعصية لا يتصور استحقاقها بالعقد فلا يجب عليه الأجر من غير أن يستحق هو على الأجير شيئا – إلى أن قال – وإن اعطاه الأجر وقبضه لا يحل له ويجب عليه رده على صاحبه اهـ.
Allah knows Best!
Darul Uloom Deoband