From a Socialist perspective, the answer to your question would be, yes. The civil "rights" embedded in classical-liberal governments since the bourgeois revolutions are fundamentally property rights and fall under the social relations we would now call "economic," formerly "political-economy," as set forth by Adam Smith and others.
As Conifold points out, however, "left" and "right" are relative terms originating in the seating of the French National Assembly, where they fluctuated in political outlook. Originally, the "right" favored the monarchy and the "left" favored the liberal bourgeoise. Even then, the "economic" property relations under law were central, manifest in royal extremes of inequality and inherited wealth that, as Thomas Piketty has demonstrated, we are once again approaching.
Joseph Weismann is right to state that "left" broadly favors progress towards greater equality, originating in the "universalist" Stoic and Christian traditions, and which taken in a modern secular sense must include progress towards "economic" equality rather than greater inequality. The "right," broadly, favors greater inequality and "natural" hierarchies.
The right will usually define this as "meritocracy," while shifting the meaning of "merit," from sheer violent power, to divine right, to birthright, to capital accumulation, etc. But there is always a "rightful" minority legally enabled to dominate the majority with the aid of force, fear, law, money, rhetoric, and mythos. Such domination will inevitably include a much greater share of property and other wealth.
But "conservative" is a misnomer. Since the various bourgeois revolutions, both capitalism and "right-wing" political movements have been largely revolutionary, uprooting traditions, cultural ties, common property, accepted beliefs, so that "all that is solid melts into air, all that is holy is profaned," as Marx put it.
The value of actual "conservation" of nature, species, or indigenous communities, for example, is more associated today with the "left."
Of course, all of this is greatly confused by the practical realities of history. The political-economic liberals of the 18th century were the anti-monarchical "left" side of the French National Assembly, while their offspring, today's neoliberals, will help overturn democracies to install bloody "right-wing" regimes like Suharto or Pinochet, in the name of "freedom" (complete with "economic" assistance from Milton Friedman and his students)! Meanwhile, "left" wing parties seeking "equality" for workers will reproduce violently dominant parties.
The present case of "identity groups" under the umbrella of a basically neoliberal Democratic Party does perhaps fall under the "left" ideal of progress towards equality for historically oppressed groups, yet can be sadly lacking in economic content and disintegrate into symbolic food fights. Meanwhile, union members wedded to nationalist myths are quick to vote for the very "right-wing" parties who ultimately seek to eliminate unions and shift taxation and national debt from "shareholders" to workers. Topsy turvy!
To return to your question, the "left" progresses towards an ideal (if variously defined) "equality" based on a Christian-Kantian "universality" of human recognition, communication, and moral worth. Humans as ends, not means only. It is hard to see how this could not have an economic dimension. Hence, modern "leftists" hope to progress beyond the purely negative "rights" of neoliberalism, where the Market, like God before it, determines the "rightful" hierarchies and millions can enjoy the "freedom" to sleep on the streets.