Further to this information on countries that are happy to proceed with citizen self-definition rather than strict dictionary definitions as many on this thread would prefer, I want to pre-empt some of the points that people often come back with when this data is cited... so firstly people often say that these countries are not recording sex properly, so how do we know what the figures actually show?
So to answer that, a tiny, tiny minority of these populations are identifying as trans, and there has been no dramatic change in these figures. If there are trans women in the figures for women then this would actually lower that countries performance in the inequality index, as trans women score poorly across all the outcomes that are measured, and this would drag that country's performance for women down, not artificially inflate it.
A second point some people make is that these countries did not ask their populations in a referendum about these issues, and that was unfair. The reality is the vast majority of policies in democratic countries are introduced by governments without referenda, and in fact this helps protect against bigotry that influences the popular vote unfortunately.
A third point that some people make is that we do not know the outcomes of these decisions yet as they have been made in the last few years and we're still gathering research about the impact. The reality is that the most pronounced effect of policy change occurs immediately or very soon after the implementation of that policy, so you would expect to see dramatic shifts occur around the time of the new policy and implementation, and to see this very visibly contrast to what had been seen prior to policy implementation. Thereafter you would expect to see a tapering effect occur.
For example, in a hypothetical given population you might see 500 people make use of the new rights in the first year that it is introduced, and then in subsequent years maybe 200 and then 100 and then 50 to 80 every year moving forward. If a negative effect of the introduction of a new policy were to occur you would expect this to be very striking in the immediate period after the introduction and then a tapering effects to occur. There is no evidence from any countries about any measurable negative impact on women of this policy change.
The countries that introduced these policies and are in the top four performing countries for women worldwide have stayed in these positions; if there was a negative impact on women as a result of introducing relaxed self gender ID procedures you would expect to see these countries drop down this equalities table as a result. The fact that they have not is strong evidence that these policies have not been a detriment to women.
A fourth point that some people have made is that introducing these policies has not been causative in making life better for women. Of course I am not trying to make any causative case along those lines, I am simply pointing out that there has been no measurable negative effect on women because of the introduction of these policies. We do know in general that, as the lives and well-being of LGBT people improve, so do the lives and well-being of women in a given population however.
A fifth point that people make is that different measures should have been used in the formation of this equality's index; for example, they ask why crimes against women have not been used to help form it. The fact is that countries measure criminality in different ways and so some countries might not, for example, record wife beating as a crime, and it also may be very under-reported in some countries. This would lead to data that is not robust and where cross comparison cannot accurately be performed, so it is not appropriate to use measures like this due to the variations in the reporting and the recording of crimes against women in different countries.
What we do know is that the measures that the equalities index do use tend to be very well correlated (negatively) with violence against women; so, when women are performing well economically, educationally, health-wise, and politically, they also are, on the whole, at less risk of criminality and abuse.
The fact is that those top countries, Iceland, Norway, Finland, New Zealand, have excellent track records in their performance on women's equality. Why would you think, that given their excellent track record, they are all suddenly going wrong now? Their excellent track records have not been impacted by their introduction of their relaxed self-ID policies – and these are policies that are proceeding without strict, dictionary definitions that many posters on this thread seem obsessed with, and are making use of the right of their citizens to determine their definitions for themselves.