When you accept something by faith you do so in the absence of evidence. I believe in God without any evidence. In fact, the Bible specifically states that you are more blessed if you have faith in God without any evidence.
This is a misreading of the text, imo. Jesus, for example, tells His followers to share their testimony, their evidence in their lives of their experience of Jesus Christ, and that through these means, people can believe.
To say you should believe without any evidence at all is wrong.
It's true that one should believe without physically seeing the Resurrection of Jesus, but there's something deeper going on here that a lot of people miss. God created and maintains the universe through faith. His faith precedes and causes to be the existence of all things. That's what the Bible teaches.
So God requires for some reason that mankind learn to do a little of the same, to believe first and create out of that faith.
The whole thing is related to spiritual mechanisms. One develops faith by "hearing it" on the inside first. It's more like an intuition than an objective measurement. And that's because the place where people connect with God is through their spirit, and believing by just seeing what you beleive on the outside does not necessarily teach one how to hear and believe God from the inside out, which is how it has to be.
According to Jesus, God is a Spirit, and requires that we worship Him in spirit and truth, and we cannot do that without developing some spirituality, and without intuitive faith and reason, one has a very weak spirituality or maybe not much at all.
Objective reasoning has it's place in the world, but is indeed somewhat over-rated. Much of how we actually live is of necessity first governed by subjectivity, and indeed what we call objectivity is just a subset of out subjective experience, an area of subjective experience we have learned to isolate and compartmentalize in order to produce great gains in this world, and maybe even the one to come.
But it's illusory to think of subjectivity and objectivity as dichotomy or opposites. Objectivity is just a subset of subjectivity, which is the reality of our human experience.
Take the idea of falling in love and marrying. Falling in love is not objective, for the most part. Nor is even choosing a mate, but both of these things can and should be tempered by objective analysis. You need to be careful and make sure you marry the right one, and objective reason is very helpful, and positive subset of the necessarily subjective process involved with choosing the right person and making that commitment.
The fallacy of scientific basis for belief is simple. Science is way too primitive. The technology is so primitive that even scientists themselves make claims such as testing for whether God did something is way out of the reach of science, maybe by definition.
As such, one should be highly suspicious of basing any beliefs, other than how to do something in a highly tailored technical situation on science.
As far as evolution, it by definition is going to be riddled with errors because evolutionists a priori exclude any possibilities of God being involved with the process, and exclude any reasonable attempts to detect God's handiwork or methods as off the table.