The goal of most 1970s radical feminists was to destroy the sex class of women not endlessly police the borders. There was a universal recognition that whilst women may have been oppressed due to their physical bodies this was not inevitable and certainly not a natural state. Many believed that womanhood could only be understood in relation to male dominance, that patriarchy invented and policed what a woman was. This famously led Wittig to declare that as a lesbian she was not a woman and her arguing to demolish the sex classification system - a goal shared by Dworkin and Firestone. It is no surprise that most of the surviving women involved in that movement support trans inclusions, it is perfectly inline with the writings and imaginings of most 1970s radical feminists.
As many of it's adherents will angrily point out the gender critical movement is not a feminist movement but a movement which includes feminists. It is a world away in both ideology and goals from radical second wave feminism. It is essentially a conservative doctrine that instead of calling for radical and revolutionary change accepts male violence as a biological inevitability from which women need protection in the form of single sex spaces and that the role of feminism should be to protect those spaces. They are not fighting a class war in the way Firestone understood it with the aim of destroying the sex class system. They are conceding defeat, and accepting society as it is, or as it was before trans people came along and ruined everything.