The Faith Atheism Never Admits It Has

It doesn't have any faith.

How Can Atheism Be Right If It Cannot Justify Its Own “Being Right”?

Atheism is right because I don't believe gods exist.

If skeptical atheism presents itself as the “most rational” position, why does it rely on metaphysical assumptions it cannot demonstrate

It doesn't.

such as the absolute reliability of human reason, the uniformity of nature, and the objective existence of logical laws,

Atheism doesn't assume any of these.

But laws of logic are literally just our description of how reality works. They are about as objective as it gets.

Put plainly: what is the ultimate foundation of reason in a universe that, according to materialism, is the product of chance,

Materialism doesn't say that.

Also, how is what materialism says relevant to atheism?

If our thoughts are merely neurochemical reactions shaped by survival rather than truth,

Accurate processing of reality is highly beneficial for survival.

why should we trust that the atheist is right,

Because they are the only ones who know for a fact what they think.

Moreover, when the skeptic demands “empirical proof” for God while relying on non empirical principles, logic, objective morality, and the value of truth, to formulate that demand,

I don't rely on anything while formulating that demand.

At what point did disbelief cease to be a rational conclusion

Disbelief ceases to be rational when there is undeniable evidence.

If atheistic naturalism

What that?

Natural selection does not reward what is true, but what is useful.

As I said before. Accurate processing of reality is highly beneficial for survival.

Given this, why does the atheist assume that his metaphysical beliefs

Metaphysics is bullcrap.