I think this is one of the parallel issues where concerns come from slightly different basic positions, but sometimes overlap and align.
I think many on the left will not think there is loss of freedom of speech but that there has bee a "progressive" move to protect people from offence. Based on their concept that they know better who needs protecting, and how offence is caused. Into which of course the rights and beliefs of women are never considered!
So it seems a positive move as it will give the issue of women being erased an airing, but expect to see a lot of people saying this is just right wing reactionary, and shouldn't get invovled.
(Also quite hypocritical as both the evening standard and metro regularly censor any pro GC comments on articles.)