How do we explain that some humans require far more evidence for some claims than others? Tell people that God says something and they believe.

Tell people that the paint is wet and they have to touch to believe.

If I ask people if God really made http://thegoodlordabove.com/god-talks-several-trump-supporters-need-safe-space/ people would laugh at me.

If I ask people if God really made the bible or send prophets, many will stone me for even asking their sacred beliefs.

Why?

Is fear of authority or instincts to obey the authority, or lack of personal cost of being false makes people easily believe things?

The bible and quran, for example, carries tons of authority and tend to support status quo. People would at least have incentive to pretend they believe. A wet paint doesn't. Or what?

What are the explanations?
There are at least two important factors or phenomena at play here. The first is whether the subject of the belief has real-world consequences to the believer. The second is whether the belief relates to groups to which the believer associates or belongs.

When a person's belief on a particular matter makes no functional difference to that person, he or she is free to believe whichever or whatever way without gain or loss. In this sense, it is easy for a person to criticise others for doing something a certain way when the person doing the criticism is not in the business of trying to accomplish the same goal. A person might complain, for example, that company X would be more successful if they focused on product Y instead of product Z. Having this belief is inconsequential to the believer since he or she has nothing to gain or lose from being right or wrong. A similar occurrence is when a person believes something to be dangerous without real evidence, as for example the consumption of GMO foods. Whether GMOs actually hurt you is irrelevant to a person who eats strictly non-GMO organic foods. Granted the person has no shortage of money, the accuracy of this belief makes no functional difference, so there is little if any incentive to be honest about the actual safety record. For a person having barely enough money to buy food, on the other hand, the actual safety record of low-cost foods is much more pertinent and important since the decision makes a substantial difference in financial burden. It is easy for a person having ample money to make the claim that expensive items are substantially safer and more effective. For a person with limited funds, the truth of the matter is far more important.

In the case of wet paint, if there is a risk to the person of getting the paint on his or her clothes, then the person is likely to see real consequences in the reality of the matter. Hence, there is little room for carelessly choosing a belief -- the truth has real consequences to this person.

A person's affiliations and group identity may be given high priority, especially when a person stands to gain from that association. Any attack or perceived attack on the group or its collective beliefs may be taken as an attack on the individual. The group may be seen and felt as an extended self. A person having no such association or feeling toward a group or its beliefs is not likely to be much offended or protective of those beliefs. Hence, he or she is free to consider their truth or falsehood. Someone whose life and well-being depend on that group or set of beliefs, on the other hand, is not going to take skepticism lightly since it poses a very real threat. In this sense, the situation is similar to that mentioned above about consequences. If a person depends on a group or belief-system for material or emotional well-being, then any attacks on that group's reputation or status may harm the person indirectly.

Naturally there is a third factor where certain religions impose or threaten penalties for those who do not defend the religion and its beliefs. In this case, a true believer may protect the group and its beliefs purely out of fear for said consequences.

To answer your main question more directly, those for whom knowing the truth is more consequential will require greater evidence than those for whom knowing the truth is irrelevant or even harmful (whether materially or emotionally). A person dependent on a group for material or emotional support is more likely to believe in that group and its teachings, regardless of the truth.

On a side note, even science can be seen as a group identity these days, from which we can expect that some individuals would derive emotional or material well-being. Having an emotional stake in science would make a person require more evidence to the contrary before considering a religious perspective. Unfortunately, this type of group identity can blind individuals on both sides of the science/religion debate, among other debates (politics, GMOs, et cetera). Ego and emotion, when left unchecked, can be very harmful.