I am discussing the political issue more than the specific case. This has been an issue in many workplaces, most relevant in schools and offices of public officials.
You seem to want to create a right to hang flags and other such items at one's workplace. You want this to be OK for some and not OK for others. You want the school or other employer to have policies that you agree with.
1) I do not believe that anyone has a right to hang a flag in his or her office. And, yes, I strongly support the positions of BLM, and would just as strongly oppose any BLM flags being displayed in a public office space. BTW, this is an issue in the DC offices of senators and House members.
2) That being said, I can understand that some employers might want to accept such displays. I think that they leave themselves open for constant bickering among their employees, and the need for committees, appeals and lots of other wastes of money and time.
3) if you think that NO ONE would want to hang say a Palestinian flags in the offices at their state university office, I can only say that I disagree.
4) What flags are OK? the ones that you choose? the ones that the school chooses? the ones that the school board chooses? the ones that the state legislature chooses? I would think that it might be considered fair for the school board to make these decisions. Perhaps it would be more democratic for the elected officials to set such policies at schools in their state.
5) I well understand that you believe that affirming the rights of homosexuals and welcoming them and their views is not controversial in a school setting. Have you lived in the US for the past 30 years?
BOTTOM LINE
Let us accept your premise that flags should be allowed, and they must they cannot violate certain standards. Are you OK with the local school board deciding what the standards are? Surely, there are no national standards for what should be allowed to be displayed at a local workplace.
What if the local school board decides that is allowable to fly the Confederate flag?
Let's be clear, there are two options
1) this is a free speech issues, and any flags not inciting criminal behavior must be allowed
2) this is a workplace issue and the employer (or someone else) has the right to set standards
Did you read the story? They only advised her against it, they didn't prohibit it remotely, which is a basic application of a general versus a specific rule
So they shouldn't have even had the accompanying message that everyone is welcome? Seems like that would go too far in repressing anything that would seem like a personal view rather than something that is common and humanitarian.
It is not a partisan flag, the others you mention explicitly are, linked to a specific ideology and not often one that is remotely positive in nature (who's going to advocate for freaking ISIS, a paramilitary terrorist organization and think that's a free speech thing in school?)
Not all flags are equal, that's where you're oversimplifying, because politics is not innately partisan. This would be like acting as if BLM is just all Marxist because a particular group (not the only BLM group) said as much in their ideals or such. Advocating against racism or saying that LGBTQ people are valid is not controversial in a civil society that supposedly is about human dignity and liberty. Repressing that is tantamount to an antithetical hypocrisy that goes the "Do as I say, not as I do," route.
It's not my preferential notion here, it's applying a standard where not all flags fit into the aspect you want to shoehorn them into. And a sign that the teacher also put up is also not in the vein of putting up a partisan flag of a political group that affects policy explicitly versus one that is functioning far more as a non profit and non partisan group. Or is the idea that all are welcome something controversial and divisive?