While I did come at this form the prospective of keeping religion out of government, I do strongly agree with you that government should never meddle in people's private religious beliefs and practices, of course assuming those beliefs and practices are in now way harmful to other. I am an atheist but I do recognize that most religions can be useful tools in society. (as apposed to laveyan Satanism and scientology. They're just tools. IMHO)

I agree with you. The separation of Church and State is to say that the government has no business meddling in religion and that, by the same token, religion has no business meddling in politics. There are enough tragic examples in history to let us know this is a very bad idea. The two can operate very well in harmony if they each keep their hands to themselves. The separation of Church and State was not meant to prevent free expression (of either atheism or religious faith) but to prevent detrimental meddling. It's neutral stance, as you say, and in my opinion, that was the intent of the writers of it.

The strict separation of church and state doesn't support atheism. A politician saying, "there are no gods and all religions that believe in gods are superstitions," would be an example of stating a view that supports atheism. This would be unacceptable if done in an official capacity. But saying nothing about their personal views cannot be said to be, by default, supporting theism.

A politician stating their personal theistic views while in an official capacity is equally unacceptable. And as above, saying nothing about their personal views cannot be said to be, by default, supporting atheism.

Therefore strict separation of church and state is a neutral stance and does not support atheism or theism.