While I would find that political position abhorrent, I wouldn't expect and certainly not demand that my company issue a specific public statement denouncing it.
You don’t need to expect or demand that, although I certainly would. The problem is when a company claims they care about that issue as part of their mission, but then prohibits employees from taking a stand on that issue or even discussing that issue.
People can care about an issue without taking a stand or even discussing the issue.
This "with us or against us" attitude is precisely what makes it difficult to get along with activists.
The only reason it is "a problem" is that it doesn't conform to the long term goals of the activists. The company needs to have goals that are separate from those of the activists in order to survive.
My wager is they de facto won't prohibit any discussion between consenting and mutually interested coworkers that doesn't negatively impact their work output, which seems "fair enough" to me.