The "deep moral dimension" generally applies to group memberships that aren't (perceived to be) chosen: sex, gender, race, class, sexual orientation, religion to a lesser extent.
But you still discriminate based on sex, gender, race, class, sexual orientation and religion every day. You don't try to talk about sports with every girl you meet, you safely assume that they probably aren't interested until you receive evidence to the contrary. But if you meet a guy, then talking about sports moves higher on the list of conversation topics just because he's a guy.
Well, I actually try to avoid talking about sports entirely, because I find the topic totally uninteresting.
But! That is mere nitpicking, and the thrust of your argument is correct. I can only say that like all human beings I regularly fail to adhere to my own moral standards, and that this does not make those standards worthless.
A few examples (in approximately increasing order of controversy):
If you proceed anyway...