Bajorans don't really need faith to believe in their gods.
A few years ago I hired a surgeon to operate on my ankle, this person had previously operated on multiple members of my family, and I had faith
in the doctor's abilities.
Faith means (among other definitions) possessing confidence and trust ... in God, or in a person or in a thing. My faith in God is a expression of my complete confidence and trust in Him.
You seem to be wanting to use a narrow meaning of the term "faith
." Kira has personally interacted with the Prophets, and subsequently she possessed "faith
" in the Prophets. There no indication that her being in their presence increased or decreased her faith.
If you have faith in your spouse, does this mean your spouse doesn't exist? If you trust in your friends, does this mean they don't exist? If you possess confidence in your doctor, does this make them a incompetent fool?
Timelord Victorious, I travel to a far away land and happen upon a unique flower, and then continue on my way, eventually ending up in front of you. I tell you all about this flower, how it smelt, the sound the leaves made in the wind, what it looked like, even the taste of the blossoms. You then respond that you never experienced this flower yourself, and for that reason it doesn't exist.
But in that far away land, the flower continues to sway in the breeze.