Your comparison doesn't address the question you quoted.
There's lots of evidence for democracy. For example, I vote.
And? Does that mean that democarcy is a good thing? That we should strive for it?
Is the voice of the statistical majority of voters really the best way to make decisions about important issues?
Free will is a trickier problem. You might need to start by defining what you mean by "free". Similarly for the idea of "equality". What kind of equality?
Doesn't matter. People widely believe in human equality and free will, and much legislation is based on taking for granted that they exist - even though there is so much dispute over whether human equality and free will exist, or what exactly the terms mean to begin with.
But all this is by the by. Would you like to attempt to answer the question you quoted? You, after all, presumably believe in God for whom there is no reliable evidence, don't you? Or am I mistaken?
You are mistaken.
People believe all the time in things for which there is "no reliable evidence."
There is no reliable evidence that democracy, free will or equality exist, or that they would be good for us, but people believe in them anyway.
This is because belief in this or that is driven by a lot more than evidence. And the alternative to evidence is not "gut feeling."
Many things we believe mainly because it would be demoralizing to believe otherwise.
It's demoralizing to believe that democarcy isn't good; it's demoralizing to believe that people are fundamentally unequal; it's demoralizing to believe that we don't have free will; it's demoralizing to believe that world peace is not possible.
While people may differ in what in particular they find demoralizing, they all have in common the conviction that there are things that would be demoralizing to believe.
And this concern over demoralization isn't simply a matter of "seeking happiness over truth."
It's that our beliefs inform our actions, and are thus self-fulfilling determinations:
If we believe we don't have free will, we will act as if we don't have it - and we will feel helpless, we will deteriorate - it will seem to us that we don't have free will.
If we believe that world peace is not possible, we won't strive for it, and as a result, won't have it.
If we believe that democracy is no good, we won't strive for it, and we won't have it.
Etc.
This is not to say that if we believe in God, then God will exist.
But it does mean that if in advance we deny God's existence, we're not likely to ever find God because we won't even try.