I've been thinking about this for the past day or two. There are a few points I'd like to make.
It seems to me that there are some parallels between blackface and drag, and a lot of them are mentioned upthread. The fact that there are some parallels does not mean that blackface and drag are identically offensive, however, and it does not deny anyone's experience.
Second, it has been said that black women have objected to the comparison, on the grounds that they feel more marginalised as black people than as women, and they find it offensive and upsetting. This is a very important point. When it is not necessary to draw attention to parallels, then to do so is simply gratuitous. If the issue can be discussed without drawing parallels, then it should be.
Third (and here I'm sticking my neck out), I think that possessing a characteristic which is seen as marginalised does without doubt give you a unique perspective and one which has to be taken very seriously. But it is not an exclusive perspective, which disallows all others. It does not give you the right to allow or disallow discussion of an issue. It also can not be used by others to allow or disallow such discussion. You can say "black women have asked us not to compare blackface and drag, so don't", but there is no reason why anyone should obey this instruction beyond simply taking it into account when making a point.
Delicate and sensitive issues need to be discussed sensitively and delicately out of sheer human decency, and it is quite possible to do so. But there are also times when a refusal to debate or resorting to insincere or vexatious rhetoric need to be faced down vigorously and directly. What I really love about this board is that it manages to hit this balance so often, which is a rare thing on the interwebs! It's why I spend so much time here.