Not sure what Angie Nixon is playing at.
If you're a member of DSA, the bare minimum answer to the question, "would you call yourself a capitalist or do you reject capitalism?" or "are you a capitalist?" is that it's false framing, and that private ownership of capital, as a social institution cum legal regime, is flexible according to society's needs; that the existing distribution of capital in American society does not, at present, benefit the vast majority of Americans; and that reform is necessary to solve problems where private ownership has dangerously monopolized resources to the detriment of the public's well-being.
To clarify my position, which I am aware is right-wing so far as left-wing politics more generally are concerned:
Property rights and capital ownership are not natural laws; they are legal regimes created by society to serve human needs. When the private concentration of capital reaches a point where it monopolizes essential resources and starves the public good, democratic government has a duty to restructure those rules. I do not believe in ideological purity or idealisms. The test of an economic system rests with its outcomes: whether the distribution of capital actually works for the people living under it.