I may be misunderstanding you here, so I'd appreciate a bit of clarification. The way I'm reading your argument, it sounds to me like your claim is something like, "Context doesn't matter: similar forms of harm necessarily carry similar moral weight." Thus, this app is intrinsically just as serious of an issue as a similar app rating women would be.
But that reasoning doesn't make any sense to me. I don't see how you couldn't apply the same argument to say "Regardless of context, it's always equally bad to violently shove someone," ignoring the difference between shoving someone standing on flat ground and shoving someone standing at the edge of a cliff. Of course I would be more upset about shoving in some contexts than in others.
So my claim is that the same reasoning applies here. This app absolutely does harm men, but the position of men in society is such that the resulting harm is fairly contained: this service is notable precisely because it's unusual. On the other hand, a similar app for rating women would be yet another contribution to a vast complex of social attitudes and institutions that combine to have a powerful oppressive effect. My sense is that network effects would reinforce and magnify the harm that such an app would do to women.
So yes, when evaluating my desire for sexual equality as a whole, I find myself more pressingly concerned about women's issues. But from my perspective, that's not an arbitrary preference but a rational choice.