Even after college exemptions were done away with the percentage of blacks drafted was higher than whites, because at federal land-grant colleges Reserve Officer training was mandatory for males. Being in ROTC meant an automatic draft exemption, since it could be assumed the students would be officers after graduation. Of personnel in the armed services, blacks were still sent to Viet Nam at a higher percentage rate than their ethnic percentage in the general population.
In addition, it was not just this which led the Black Panthers to oppose the war. Their position was that as long as black people in the US were not fully equal with whites, why should they "defend" the US? Not only that, but the Black Panther leadership was almost entirely Marxist socilaist, and considered the struggle of the North Vietnamese to reunify their country as a legitimate war for national liberation, and to gain control of their country from an oppresive elite class in the South. They viewed "police oppression" in inner cities as the equivalent of the SVN government's policies toward the countryside within Viet Nam. All of these factors led to official opposition to the war on the part of the Panthers.