Yes, children should be welcome to sit in worship services with their parents; worship is for everyone, and it’s better (and more successful) for children to get used to a church environment from babyhood rather than suddenly be expected to sit still and pay attention when they are deemed old enough, especially in today’s culture of near constant entertainment. Of course, a child’s right to be in church should not infringe on the general congregation’s need to worship in a reverent atmosphere — parents should take out babies who are crying and bring them back in when they are quiet, and children should be taught that a church environment is special and requires particular behavior — this is a matter of respect and fairness. (I have been amazed at times by parents’ level of tolerance for the sound of their own child’s crying).
VIEWPOINTS RESPONSE: Children should be welcome
On the other end of it, even after 50+ years I can remember how hard it was for my (undiagnosed at that time) ADD mind to sit and be quiet in church during childhood. Parents should bring quiet toys or books to hold their children’s attention during a long service, supporting the children’s gradually increasing abilities. Church should not be a torturous experience for children by parents demanding behavior that is above the child’s level of ability. The point is for children to enjoy church and want to be there, not to dread it.
Of course the culture of individual congregations should be respected and if a parent is in a “no children” congregation, it’s better to investigate changing the policy through appropriate channels rather than disrespecting the congregation by inflicting fidgety or noisy children on them when they clearly have different expectations.