Based on your interpretation every group could simply be redefined into illegitimate.

• We are for democracy
• Oh so you think that monarchy is bad and you want to define yourself as excluding loyal subjects of the king! That will never be legitimate.

Leftist think that democracy should extend into the economic realm as well and what we should do with the means of production should be governed by the people and not just whoever happens to own the capital. One way to word that would be anti-capitalist, but another way would be to word it as economic democracy.

So if you require an inclusive definition for something to be legitimate, there you go. Liberals in America do not seek to do away with capitalism, you would be hard pressed to find any that do. If you support capitalism, then by the fact that capitalism’s private ownership is mutually exclusive with democratic control of the economy, you don’t support a democratic control of the economy.

You can’t have a vegan meat eater, not because of any moral assessment on veganism or meat eating, but because those two terms are mutually exclusive.