What type of terrorist organization (e.g., left or right wing, nationalistic, religious) is most likely to attract female members?
If protests against abortion legislation and facilities can be classed as terrorist activities, as some contend it surely can be, American women are very inclined to join religious terrorist groups. If violently sabotaging land development and attacking pro-animal experiment and pro-fur groups can be classed as terrorist activities, as such have been, American women are also very inclined to join environmental protest terrorist groups and animal rights terrorist groups.
I agree with #5 - stereotyping women (or men) as being more likely to join one type of terrorist (or any other) organization than another ignores the wide range of emotions and motivations behind any individual joining any type of organization.
Women might be inclined to join more radical organizations if they are in a setting where they have to fight to be included at all, but I think that's a really poor basis for attempting to give a generalized answer.
I think women often gravitate to environmental terrorist groups, if we are going to stereotype. They are less interested in reforming the government. They want to save the whales, or the trees, or the rain forest. I do not think it is necessarily a good idea to suggest that women would be more likely to join one group or another, because there are likely even women in radical Islamic extremist groups. I can't imagine why, and I don't imagine they would get much respect.
To expand on #3, the Weather Underground was a radical Left-Wing (U.S. model) terrorist group that was very active during the 1970s. Much of the anti-capitalist and anti-government rhetoric they preached became standard issue for other radical groups. One interesting thing about their actions was that they did not directly seek to kill people (although they set nail-bombs and other explicitly anti-human weapons) but were more concerned with "extreme vandalism" as a method of public protest. The distinction has little difference, though, and they did hurt and kill on occasion. However, they certainly did offer upward mobility to women; Bernadine Dohrn, still alive and active in teaching and politics, was the leader and public face of the Weather Underground for a long time. I'm not sure that this is a selling point, however.
I agree that women would most likely be attracted to a left-wing terror group, as they tend to embrace progressive, even radical views about gender roles. One domestic terror group (though they never took many lives) was the Weather Underground of the late 1960s, who featured many women among their founders and leaders. Accordingly, part of their ideology was a critique of the oppressive nature of gender relations in the West.
I would argue that a left-wing terrorist organization would be most likely to attract female members. This is the most radical type of organization and would be the most likely to be willing to act in ways that are opposed to the general values of society. Many of the other kinds of organizations would be more likely to want to keep women in their traditional roles and out of a terrorist organization.
Right-wing Terrorism groups generally seek to maintain the status-quo or to return to some past situation that they feel should have been conserved. Sometimes these groups assuming rightist ideologies will have ethnic/racist characteristics too. Violence against migrant communities also comes under this category of terrorist violence. Examples of these are: the white supremacy movements in the US known as Ku Klux Klan (KKK). There are many women involved in this terrorist group in the U.S., how would you explain their attraction to the right-wing?