In this modern era, everything can be questioned. Traditional answers have no power to convince the skeptic; we no longer collectively assume and share a coherent reality, and we are capable of doubting any proposed order to our existence. Anyone who really pursues these questions comes to recognize the possibility of meaninglessness, of nothingness beneath it all.
So what does faith look like in this modern period? That depends on how one is approaching existential doubt.
Though Tillich identifies doubt and meaninglessness as the dominant anxieties of this era, it seems to me that everyone does not bear these to the same degree. Some, though aware of at least certain questions, succeed in putting them aside sufficiently to not feel the threat of meaninglessness.
Others may simply refuse to look too hard at any such questions, perhaps realizing everything may collapse if they do. They select for a framework that offers meaning, a way of living coherently, while cognizant of an inherent fragility they don’t want to examine.
What we are all doing is a very modern thing: because of our individualism and unmoored existential reality, we are choosing. As Sartre said, speaking of our lived experience, “man is condemned to be free.” He was referring to the burden of having to choose.

We all must find a meaningful way to live; how we can have the courage to be, by identifying with a particular system of belief that offers us belonging and meaning. Everyone does it. The possibilities run the gamut from going down a rabbit hole of conspiracy theories to identifying with an older traditional religious system and structure. One can latch onto the conspiracy theory birthed yesterday, choose a medieval framework older than modernity, or even go further back into antiquity and be a Druid. We are modern people choosing individually, and sometimes opting to give up our individualism.
We have a tremendous will to believe what we choose, and the capacity to convince ourselves. Sometimes we call it rationalization, or even living in denial. If the stakes are sufficiently high, we may convince ourselves of many things. Though this can be a practical and somewhat effective approach, ignoring the most threatening questions, it comes at the price of foregoing the pursuit of truth no matter where it leads.
Another possibility is that a person may have a mystical experience, an encounter with the transcendent, which moves them beyond themselves and grounds them despite their doubts. Do they still choose? Yes, one must choose to trust the experience!
For this person, the questions do not simply vanish, but one now has something known individually, internally, by experience, which is meaningful. This knowing which transcends argument and evidence, tradition and dogma, can be a bulwark against persistent doubts.
We cannot choose to have such a subjective experience. The message in the modern era cannot be to tell people to have a mystical experience. If that were the only way to escape doubt, we have all the more reason to be cynical and despair.
We must consider those who squarely face the unknown, whose doubts are ever-present, who see the fragility and weakness of traditional frameworks of the past, but also have not had a mystical encounter. Is there anything to say to them? The atheist, the skeptic, the one for whom every authority and institution is questionable, they desire to doubt but they cannot help but be aware of the uncertainty inherent in our existence.
These are those Tillich is thinking of in The Courage To Be. The anxieties of doubt and meaninglessness are most pressing for them, and they cannot simply will them away.
