That only Americans have the right to participate in our political system is an expression of values. And it’s entirely compatible with democracy. The citizen versus non-citizen distinction is fundamental to democracy.
Do you think the first amendment means the government has to allow in immigrants that are Nazi sympathizers? What about Communists?
Americans have free speech. But Americans can also decide which foreigners are allowed the privilege of being on American soil. In fact, I would say that it’s precisely because we have free speech that we must carefully guard who is allowed into the tent.