I wonder if it is all part of what the Woke see as the ongoing battle between the oppressor and the oppressed. Any exclusive club (such as that of biological women) is automatically oppressive, and their knee-jerk response is that any boundaries that prevent the 'oppressed' from entering said club are illegitimate and must be broken down, no matter who the 'oppressed' are and regardless of any safeguarding concerns this could entail.
Yes, this is what people like Jordan Peterson call cultural Marxism. Which isn't a real thing, quite, but it's meant to be a description of what you are pointing out. A Marxist class, applied to almost any kind of group or category, with an assumption that one side is being oppressed, and the idea that by destroying the grouping it will create justice.
Thinking about it that way, it becomes easier to see how the left has been drawn into this type of thinking, even about a biological difference between the sexes. How often, for example, does a feminist analysis assume that women more often end up as carers because of class oppression, and somehow if the right conditions were achieved there would be a balance of men and women in such roles? Despite there being no strong empirical evidence for that, and some reason to think it may be false?