Nazis were proud Socialists. Not "Conservatives."
Conservatives are mostly religious nuts. However, most of the Nazis were non-religious, with some even being atheists. They never gave any importance to religion.
As for conservative, there are various uses of the word - fiscal conservative, social conservative, etc. The European definition of "progressive vs conservative" differs somewhat from the American one.
In Australia, you have a conservative and a liberal political faction. And the conservative side is obviously not religious nuts.
In the US, there is almost no correlation between conservative and religion, although the reverse is not true. If you look at a group of highly religious Christians, you will find today they lean Republican. But I personally know of many religious nut-jobs that somehow find it within their value system to go Democrat.
Go figure.