After WWII, German fascists who had nowhere else to go were absorbed by the right parties (unlike in other European countries where the far right was present but fringe). It’s only now that the AfD has broken out into the open, but fascist-leaning sentiment has been at least a small part of the CDU forever.

They’re just a regular conservative party, the pivot to being bloodthirsty racist fuckbags is somewhat recent. Angela Merkel was in this party as well and she was pretty open to immigration and specifically hates the current party chief.