I think there's a failure of communication here because Americans[0] tend to conflate "liberal" with "left" although liberalism is not at all leftist and is far more compatible with right-wing ideologies than leftism.
In the most general sense left-wing ideologies are about abolishing hierarchies whereas right-wing ideologies are about either sustaining or enacting them. The difference between liberalism and conservatism is that the former promotes hierarchies that follow from property rights and the latter infers them from tradition (e.g. God's will or "natural order").
Just like anarchists and state communists can have leftist infighting it's possible for there to be infighting on the right. As the US has literally spent decades fighting leftist ideologies, the predominant political discourse in the US takes place between different flavors of the right.
No major media outlet in the US will promote abolishing property ownership or collectivising the means of production. When we talk about "leftism" in US media this usually refers to socially progressive ideas like public healthcare, individualist attitudes to anti-racism, LGBTQIA+ rights and so on. While these ideas naturally follow from most leftist ideologies, they're not addressing the underlying social hierarchies or systemic criticism. Case in point: abolishing the police is a systemic critique if taken literally, but in the public discourse this has been reduced to police reform, which is about tweaking the system, not replacing or abolishing it.
[0] While this is not unique to the US, I'm focusing on the US here because of the original context. There are more discussions to be had about how this presents in other countries and how the Cold War affected those but this is not the time.
It might be a good summary to say that Greenwald is intensely liberal in his stance on civil rights, so much so that he doesn't fit on the American liberal-conservative spectrum on this issue. He's willing to compromise with both liberals and conservatives to help get his message out. His overall stance is not left wing, because most of his other views (at least the stuff he emphasizes) are more (American) libertarian or liberal/conservative, not genuinely left wing.
In the most general sense left-wing ideologies are about abolishing hierarchies whereas right-wing ideologies are about either sustaining or enacting them. The difference between liberalism and conservatism is that the former promotes hierarchies that follow from property rights and the latter infers them from tradition (e.g. God's will or "natural order").
Just like anarchists and state communists can have leftist infighting it's possible for there to be infighting on the right. As the US has literally spent decades fighting leftist ideologies, the predominant political discourse in the US takes place between different flavors of the right.
No major media outlet in the US will promote abolishing property ownership or collectivising the means of production. When we talk about "leftism" in US media this usually refers to socially progressive ideas like public healthcare, individualist attitudes to anti-racism, LGBTQIA+ rights and so on. While these ideas naturally follow from most leftist ideologies, they're not addressing the underlying social hierarchies or systemic criticism. Case in point: abolishing the police is a systemic critique if taken literally, but in the public discourse this has been reduced to police reform, which is about tweaking the system, not replacing or abolishing it.
[0] While this is not unique to the US, I'm focusing on the US here because of the original context. There are more discussions to be had about how this presents in other countries and how the Cold War affected those but this is not the time.