Does the Left-Wing Christian really exist? I think not, if we mean someone who equates leftism with Christianity. People like Garry Wills are not now and probably have never been Christian in any meaningful sense of the term.
They simply put a veneer of Christian imagery on the banalities they have picked up from Marxist professors. I would say there are whole denominations–the United Church of Christ, for example–of which this can be said.
There are, of course, Christians who swallow the lies of the Left, just as there are Christians who have swallowed the lies of every dominant political class, whether the lies are derive from capitalism or from monarchical absolutism. I would say, however, that the monarchist lies have some congruity with a Christian view of God the Father, and that the lies of capitalism are consistent with a Christian insistence on moral liberty. Leftism, being a revolution against the created order and human nature is far more destructive, but I agree for the sake of argument that an otherwise good Christian might be taken in by Leftism.
That having been granted, there is no quarter to be given people who insist on cloaking their leftism–Marxist, feminist, homosexualist, one-worldist, environmentalist, vegetarian–in Christian garb.