That is not what the amendment states.
"Congress shall make no law respecting an establishment of religion"
Congress may not make any law establishing a [national] religion in the United States.
"or prohibiting the free excersize thereof;"
Congress may not make a law which restricts people from practicing their religion.

Remember the context of the situation: many people left Europe for religious freedom. At the time the idea was not to remove religion, but to prohibit the government from restricting religion.

Also:

I did not say, nor did I say that the Amendment said, that the idea was to remove religion. I simply said that the idea was for the two entities to be independent of each other.

So while a politician makes decisions about his country, he does not have to do so under the influence of a religion that he does not endorse. Instead, he may make logical decisions about his country... and go home and worship any god (big G little g).

Actually, that is not possible. Religion is also a philosophical guidance, and a politician who is religious will undeniably have 'religious ideals'. What it realistically means that it does not officially endorse religion, and that officially, it is a seperate entity. When you get into politics, theres official and non-official (which is bullshit)- and a ton of politicians are religious- and a ton of their decisions have religious ideals included.