No one is denying 'our sisters' the right to online activism, it's just that there is a world of difference between activism and bigotry
Social media clauses deny those who sign them, as a condition of their employment, the right to any form of online activism their employer regards problematic. So yes, they do prevent online activism to women, disproportionately, in a political world which men dominate.
Also, one persons bigotry is another’s core belief. I believe sex to be an immutable characteristic, that one cannot change sex, and that women deserve and need single sex spaces.
Were I to campaign for the right to withdraw my child from RSE, because of my GC beliefs, would I also deserve to be sacked? Or is it only Christians who do..