Most of the "beliefs" you refer to actually don't have to be beliefs at all. They have no practical consequences; they don't change anything about what the person who claims to have them actually does. Such beliefs don't have to have their evidence weighed because they make no practical difference. When people say they "believe" them, they don't mean they're actually using them to decide their actions; they are just signaling.

For most beliefs that do have practical consequences, people do weigh evidence for them. However, this does suggest a clarification to the characteristics I gave for religions and ideologies: that they start from beliefs that are in the "don't have practical consequences, so saying you believe them is just signaling" category, but then use them to justify beliefs that are in the "do have practical consequences, so should be judged by weighing evidence" category.