Honestly, I think it does a disservice to the fight against racism for black people and Jewish people to find solidarity in this.
I don't agree with this statement at all. You said yourself that some blacks are anti-semitic and some Jews are anti-black, which is precisely why the solidarity is a good thing. Regardless of the difference in particularities between the two, they can stand together because they both have been victimized by bigotry. You're suggesting that they should keep separate and emphasize their differences rather than the commonalities. That is precisely why you'll find some cross animus between these two minority groups, or any two minority groups for that matter. In fact, it's precisely why bigotry exists to begin with, because there isn't enough solidarity among people of different ethnicities.
I personally found it unsettling that a solid majority of blacks in California voted for banning gay marriage a few years ago. Given the anti-miscegeny laws they faced in the past, you'd think they'd show some solidarity. But unfortunately the fact that black people in America are more religious on average than white people proved to be the ruling factor. There was a lack of solidarity here, and as a result, gays were denied equal rights for several more years in California. This is an illustration of precisely why solidarity among various minority groups is more a good thing than a bad one.
It's true there's some group of white supremacists in America who hate both. Probably not in higher quantity than Jewish people who are racist against black people (I've known some) and black people who are anti-semitic. But I don't think these white supremacists are much of the "problem" for black people or Jewish people in America today.
You probably see it that way because you don't think the white supremacists can have much of a direct material effect, that what they are doing with the swastika is purely symbolic, i.e. sticks and stones. But these images are offensive. It reminds people of things like slavery and genocide, and makes them feel like they are in a hostile environment. You probably don't get this because nothing in your background or experience would make you feel personally offended at the symbols so you aren't sensitive to it.
The problems are a lot more subtle and pervasive. They have to do with how every day people form subtle biases that influences whom they see as capable or threats and they have to do with who is born into what money. And in these categories Jews and black people could not be further apart. I haven't lived in Missouri so I don't know what kind of crap Jewish people have to deal with, but I really doubt it's anything like what black people have to.
Differing circumstances doesn't mean they shouldn't have common cause. Certainly the bigots would prefer it that way - divide and conquer.
This bogeyman of random swastikas is exactly the wrong thing to let dominate the public consciousness. These things are like the anti-semitic statements you find all over youtube. On the face of things they seem really terrible and like something that needs to be stopped, but in reality they're just the ramblings of ineffectual idiots. People who don't actually have power or influence in the real world so they try to do something shocking to get noticed. Like drawing swastikas in feces on bathroom walls. Frankly I would say these things are best ignored. Throwing a media circus over it and getting the head of the school fired while the person who did it goes uncaught is probably giving that person exactly what they wanted. Regardless of what their sincere opinions are.
This isn't only about a single swastika. There was more than one incident publicly identified, but most racist incidents are never reported to anyone. Frankly, I have no reason to disbelieve both white and black students who claim they hear the n-word on at least a semi-regular basis at Mizzou. We've had posters in this very thread with direct, personal experience with Mizzou and other southern universities say the same thing. I have no reason to doubt the veracity of any of it. If we're going to insist on a photo or audio recordings to prove every case of a spontaneously shouted slur then we are willfully and intentionally putting our heads in the sand.
So far as the university president, I lean toward agreeing. It's tough for them to do anything about the racism without censorship, which is something I oppose. I think these students are complaining about a circumstance which is real, but misplacing their anger toward the person at the top. Unfortunately, it is a fact of life that when bad circumstances exist within any group or organization, the person at the top tends to be blamed even if they couldn't have done much of anything about it.