I think feminism is about giving men and women equal opportunity in society, politics and economics. There seems to be the idea in popular society that it is about equalism - as in women and men ought to be treated exactly the same - but I don't think that really addresses the point. Then you end up with never-never land people asking irrelevant questions like, 'should men hit girls now during a dispute now? That is equalism!' (You might have to point out that this is already the case anyway
). Feminism is more about giving women the opportunity to pursue social, economic and political power so that they can make the choices that are important to them.
I think the unisex sports thing is a little irrelevant. I don't think the majority of people would actually care if professional sports teams are unisex or not. Most feminist discourses around sports involve giving women the equal financial and political support so that they can pursue atheletic careers. In Canada, for example, there was some controversy over how the women's Olympic teams were receiving far less support then the mens' teams.
In terms of work, on the other hand, I've heard plenty of people make dubious claims about how physical strength 'naturally' segregates men and women into different roles, when in reality, stereotypes associated with those roles (i.e fire workers, police officers) act to reinforce male privilege in the labour market. IF you think you only need brute strength to be a police officer, you are going to fail miserably at the academy, trust me. The type of skills you need go far beyond strength.
I also often hear people make reference to hunter-gather societies to further 'prove' the natural segregation between men and women in terms of work without realizing that this premise is only true if that society conceptualized hunting in a manner that excluded women. Some societies relied on brute strength (spear throwing lets say), which privileged men (and yet, that again depends upon how you are conceptualizing 'hunting'. Is hunting the mere act of throwing the spear or does it involve the whole process of making the spear points, preparing the meat - activities that women did). However, there are some other societites, like some Aboriginal tribes in Canada, that relied on another method that basically involved herding animals (i.e buffaloes) off of cliffs or into traps where they were shot to death with arrows. Women did participate in this form of hunting.