It's not true that feminists don't care about men being discriminated in the job market, SOME feminists do. It depends on the definition and mission of feminism they have.
Some feminists - especially in the third wave - fight for the end of the gender bias system. This system affects men, women and also people who don't identify within the gender binary. Basically: everyone.
That gender system is what conditions men to be perceived as more "able" and autonomous than women. That's why it's not well perceived when men work as secretaries, primary school teacher, nurse and other perceived "women's" job. I read a study for a research paper on the subject. Unfortunately I did not keep the article (d***!) because I did not think I could no longer access them after finishing my studies... But here's the abstract :
"Occupational segregation by sex remains the most pervasive aspect of the labour market. In the past, most research on this topic has concentrated on explanations of womens segregation into low paid and low status occupations, or investigations of women who have crossed gender boundaries into mens jobs, and the potential impact on them and the occupations. In contrast, this article reports on a small-scale, qualitative study of ten men who have crossed into what are generally defined as womens jobs. In doing so, one of the impacts on them has been that they have experienced challenges to their masculine identity from various sources and in a variety of ways. The mens reactions to these challenges, and their strategies for developing and accommodating their masculinity in light of these challenges, are illuminating. They either attempted to maintain a traditional masculinity by distancing themselves from female colleagues, and/or partially (re)constructed a different masculinity by identifying with their non-traditional occupations. This they did as often as they deemed necessary as a response to different forms of challenge to their gender identities from both men and women. Finally, the article argues that these responses work to maintain the men as the dominant gender, even in these traditionally defined womens jobs." (Cross and Bagilhole, 2002)
From what I remember about the article, men in such occupations would rather say they were "medical assistant" than "nurse" or say "I work at the library" rather than "I'm a receptionist".
So that's how the gender system affects men into pressuring them to find a "better" job than women and it's so it's a burden who a man who has chosen a dominant female job. These burdens can stop once we stop believing that genders are opposites and completely different. In other words, fight the gender assumptions!