That would be taking it to an extreme. However, parents are responsible for the safety of their children; that means being alert to issues, never ignoring a child that is upset about another adult, and teaching age-appropriate information to your children concerning their personal safety to assure them that if they are uncomfortable around any adult, they can come to you as the parent and tell with no reprecussions.
Not all or most, or even a large minority of adults are abusers. However, it only take one, and the damage can be incalcuable. It may be a family member that didn’t abuse you as a child, but you were not the sex they pick on; you have a child of the opposite sex and they may be at risk.
People need to use their brains for something besides keeping their ears apart. It is not at all unlikely to have a family where there has been no abuse; it is also not at all unlikely to have a family where one or more relatives who may be abusers. The world has not necessarily suddenly descended into depravity; it (sex abuse) existed before, but it was one of those things “people didn’t talk about”. Whether or not there is more abuse I will leave to someone else to tally; but the point still is that children have a right to be safe and it is the responsibility of the parents to provide that.
Trust is not trust if it is blind to the fact that people are human, humans sin, and one of those sins is sexual abuse against children. Blind trust is just another definition or either ignorance or naivity. No, not everyone does it. But just because someone is related to you or has been your neighbor for 10 years or is the popular teacher/coach at the local school does not mean they are not the source of damage to your children.