Well ... then disobey!
I did not, by the way, attend this march and it's not something I would have considered attending. No, I don't support antisemitism, but I also most certainly do not support the Israeli government and the IDF and would hence never entertain attending any event that is bound to be a flood of Israeli flags and for which the official twitter/X account of the state posted "thank you" earlier.
BUT: I fully support the right of anyone who feels differently to attend. And, yes, that absolutely includes employees. Almost all of us are employees of some company or other. And, no, they do not get to tell us what we get to say or think, or what our politics ought to be!
This is something I feel incredibly passionate about! It's also, literally, a human rights issue! People should not be forced to pick between supporting a cause and their ability to pay the bills. That's just ... insanely wrong on multiple levels!
FWIW, my own employment contract makes a multitude of stipulations as to what I can and cannot supposedly say or do in public. I breach them if and when I please and would advise anyone to do the same. An employment tribunal for "so ... I have political opinions" is one you're almost guaranteed to win, so long as your opinions fall anywhere within a reasonable spectrum.
TL;DR: not a protest I would personally attend, but: BBC staffers should be able to, and I would recommend to anyone to "just go anyway" (but also: get a solicitor first)!