As I say, I think pro- or anti-capitalist would be better, as it would identify the truly significant ideological and political division more accurately than the C18th spatial metaphor.
One problem with the Left/Right terminology is that it allows subsiduary matters to obscure the main issue. I think the "Left's" involvement in identity politics has caused all sorts of problems in this regard. We can see it all over these boards, and all over every similar discussion group or political movement: everyone furiously scrutinizing each other's words for some verbal slip-up that might reveal them as "really" on the "right" because of some secret or unconscious prejudice or other. And pretty soon we're in a situation where "Left-wing" just means "tolerant" or "nice" or "decent" (as people here tend to put it). The term loses all significance.
The real problem is capital. Nothing else will be solved until that is solved. So I think we should concentrate on the real problem. And the Left/Right metaphor is a distraction from that.