Doesn't this apply to most people as well? Most people are happy to vote for rent control - unless they're a landlord. Most parents will vote for higher property taxes if it means better schools, but most childless homeowners will not. Most urbanites will vote for gun control, most hunters will not. People who walk or take public transportation to work will vote for higher gas taxes, people with 2 hour commutes will not. Heck, isn't one of the claims leveled against liberal white suburbanites that they will happily fight for minority rights in the abstract, but then fight for zoning codes that in practice keep minorities (other than high-earning Asians) out of their neighborhoods anyway?

Social movements that succeed tend to take this into account, and frame things in ways that are not zero-sum. I lose nothing by letting gays marry; my heterosexual marriage is still just as legitimate. I lose nothing by allowing abortions - as a male, I'm not going to get one anyway. I lose nothing when YC seeks out qualified minority & female applicants; I have plenty of advantages of my own, I don't need that extra attention. I lose nothing when Black Lives Matter - my life still matters too, we just need to fix the institutional systems that let a black person get shot dead with no repercussions to the killer. (Personally, I think the left has made some very large tactical errors recently by ignoring this principle - fights over things like affirmative action, political correctness, and white privilege are all because the debate has been framed as "You must lose something in order for life to be fair", which isn't a great way to persuade people.)