As per the excerpt of the article in this post:
But the law isn’t listed in the 33-page candidate requirement guide and there is no space on the petition paperwork to list any former names.
So it seems to me that it's a law that in practice bans running within five years of (non marriage) name changes. Whether it's unevenly enforced or not it clearly hits trans people disproportionately.
I agree with your sentiment, but I have to push back on Hitler not relying on religion. At the very least he used religion to get his population with him. As far as I remember his religiosity has been questioned as being sincere or not, but he himself never claimed not to be christian if I'm not mistaken.