For any one ideology A to be consistent with another ideology B, then principles which are necessary for B must also be necessary for A.
This doesn’t work for atheism as related to conservatism. There is nothing about atheism which requires the inclusion of individual sovereignty.
Thus, while the principle of individual sovereignty is necessary for conservatism, it’s not necessary for atheism.
Atheism is not consistent with conservatism.
As for the other, Christianity does not necessarily require that the government collect taxes to create a welfare state. This is consistent with conservatism.
Liberalism necessarily requires it though. This is inconsistent with Christianity, which doesn’t.