Taxation isn't a given starting point. There is a big difference between "giving" and "not taking". The burden of justified action falls on the one initiating the action. In this case, people want to use the government to take money from churches. When framed this way, this violates separation of church and state. The question would then be whether the government has authority to cross this boundary.
If the default is to tax organizations, it is not a question of "people want(ing) to use government to take money from churches", but more that it is inappropriate to give money (tax breaks) to organizations that have a bias against the common good (redistribution to members of a congregation vs. all citizens).