coherent liberalism must also oppose capitalism, and capitalism is inherently non-democratic

Yup, and I hate that "liberal" for most people means something completely different. I self-identify as a liberal, in the sense that, for example, a rentier class of landlords existing or that any human's existence being completely dependent on their job and income is inherently counter to liberal ideals.

I don't know when someone decided we'll mean something anti-liberal by the word "liberal" but they can go fuck themselves.

I don't think democracy is inherently liberal or not, and I don't think it really matters? This is a question of outcomes. No other political system has a history of consistently producing relatively free states (as in freedom for the people within the state). All other systems, be it oligarchies or dictatorships, even if they result in a short period of stability and freedom, almost universally deteriorate into authoritarian hellscapes over time. If we can come up with a system that is better at preventing oppressive regimes then we should rally behind it, but currently only democracy has a positive track record there.