Are Nonreligious Organizations Able to Provide the Same Services as Churches?

[Nope]

A secular organization like our government?

I don't know. Maybe. The government generally only provides certain things to the poor. Churches provide them to a lot of different people regardless of income.

Talking to my friends, the social aspect of church seems to be one of the selling points of attending. They can meet new friends or let their kids leave their side while someone cares for them for free. Of course, there is more than just childcare available at churches. My friend's church encouraged people to host small bible study groups in their house. From what I understand, the groups were less about the bible and more about the free food and social interaction

Perhaps there would be less religious people if such needs could be somehow addressed. I just don't know how that would work.

Edited to add this: We tend to accept people's word when they say that they attend church for religious reasons but I think that a lot of people go to church so that they can get help, meet new people, get free child care, have a safe place to send their teenagers etc.

Sometimes things just suddenly click in my head that should have been obvious and I feel stupid for not realizing it sooner. Maybe the reason that religious people in the USA are so against the government providing more services to people is that church leaders know people will turn away from religion if they have other options to meet their needs.