Even if one rejects the argument that capitalism produces fewer inequalities than other forms, there are still other reasons for those on the ideological left rethink its relationship with it. For example, as Steven Pinker has noted ("The Better Angels of Our Nature: Why Violence Has Declined"), the spread of capitalism has probably contributed to the downward trend in violence that we have enjoyed over the last few hundred years. Why? Because there's little incentive to kill others when you have a profitable trading relationship with them.
And then there's the issue of gay and lesbian rights. As a recent (June 2014) editorial in the conservative Roman Catholic monthly, New Oxford Review, notes, one of the primary movers behind same-sex marriage has been big business. Quoting from an article that appeared in the magazine two years before, it notes that
When it was first seriously proposed a decade or so ago, same-sex marriage encountered strong opposition from most Americans. But today, traditionalists find themselves on the defensive, and this is a battle they appear to be losing. While many factors account for this, a major one was the entry of a powerful new combatant into the fray: Big Business. Corporations such as The Home Depot, Target, Microsoft, American Airlines, Bank of America, Citi, Coca-Cola, and Google, to mention only a few, have thrown their weight -- and their capital earnings -- behind the push for same-sex marriage.The editorial goes on to note that when the Supreme Court heard arguments regarding the legalization of gay marriage, some of the loudest voices arguing in support of marriage equality have been Budweiser, Levi Strauss, Expedia, HBO, Kenneth Cole, Smirnoff, Nordstrom, and Kraft Foods (p. 14). Similarly, some of the biggest financial backers of the effort to defeat California's Prop 8 included executives from many of the world's largest hi-tech companies, such as Cisco (e.g., John Morgridge), eBay (e.g., Pierre Omidyar), Google (e.g., Larry Page), and Yahoo (e.g., Jerry Yang).
In short, perhaps the left needs to rethink its relationship to capitalism. It has more in common with it than it realizes.