Part of what makes blackface so horrible is the power imbalance that underlies it. In the days of minstrelry, black people were deeply and powerfully unequal in civil society. They had no recourse against the indignity done to them by blackface performance, and it was an indignity forced on them by a more powerful social class.
Try replacing nerds with black people in that paragraph and tell me it's at all comparable.
Where, in spite of that, your teachers were probably pushing you to perform, and when you got out you probably had no trouble getting into a good school which made it more likely for you to get a good job.
Kids are cruel, but their social order is not the real world. In the real world nerds are not a disadvantaged, let alone oppressed, group.
It is comparable. In the way that blackface allowed African Americans to work in venues and productions that they were otherwise prohibited, BBT allows nerds to be the subject of a mainstream sitcom.
BBT is not at all empowering the way that "Weird Science," for example, was, and highly-mainstream TV executive Chuck Lorre is of exactly a more powerful class who has allowed nerds to enter into a world where they were previously excluded. That BBT is only slighly less-awful than how nerds were previously portrayed is not a badge of honor.
How often does the show demonstrate dignified interactions between its main characters and the outside world?
Try replacing nerds with black people in that paragraph and tell me it's at all comparable.