Nobody till now knows that Karna is in fact lord Surya and Kunti's son, thus he is of a noble birth. However, it can be seen that Draupadi humiliated him based on his caste/last name. Even though she was a woman of great knowledge, she should have still not discriminated others based on their caste. The whole caste system was formed to assign people work based on their family name. However, there is no rule that one must stick to the profession that he/she does not like. And even today, we can often see racism based on the surname. If you are born in a Suta family does not mean that you are a lesser being. Had she be born in Suta family instead of the noble family, would she say the same to the guy from the noble family? Nevertheless, she should have been mindful about Karna's feelings and he even a noble at that time since Duryodhana made him a king.