the day without women thing is a little bit different than the day without immigrants thing because at least the issue can be openly discussed without fear of deportation.
regardless, one has to realize that a day of action is not a strike. strikes are not effective because they appeal to a sense of morality or uphold a concept of righteousness, they're valuable because they deny productivity to capital, or, better, because they shut down production altogether.
if this day of action were a prelude to a general strike, i'd heartily endorse it and actively organize for it. but, that is not going to be what happens.
this is consequently at best a waste of time.
but the reality is that there are going to be ununionized women that are going to get fired, and they will have few legal options at their disposal, if they can afford them. you have to weigh a complex of things together, including long term pr issues and even the views of the employers. but, if anything, employers are going to have less incentives to not fire women that walk out because they don't have to worry about getting busted hiring illegals.
people that want to talk about free speech don't understand what free speech is.
co-ordinated strike action is necessary. but, that isn't what this is, and it's absurd to think it is.
my suspicion is that this is another government sponsored sting operation, and that it's being organized as an opportunity for capital to fire women that walk out. if you walk out and get fired, you've fallen into a trap that was set for you.
but, hey, weigh your own risks and come to your own conclusions.